Understanding Simple Equations in Algebra

[Music] [Music] hi everyone today we're starting with simple equation and my name is Ravi Prakash okay simple equation is a very important topic in algebra and in this quant write the simple equation does not mean only forming equations we will discuss lots of things is simple equation right let me tell you whatever things we'll discuss in simple equation okay so in simple equation first thing we'll discuss is condition for unique solution condition for unique solution and no solution okay second thing we'll discuss is forming equations forming equations okay third thing we'll discuss is reciprocal equations reciprocal equations fourth thing we'll discuss is discuss as problems on digits right and then we will discuss it through lots of questions lots of questions right also we'll discuss this three equations and two variables cases three equations and two variables cases right so these main things we'll discuss in simple equations with lots of questions so this very important topic I'll discuss maybe some people teases in a number system or some in some depth look you'll find this in other chapters right but all these topics are related related to forming equations and solving the equation right so we keep it in this simple simple equation and a simple equation right so now let's start simple equation now see here any equation of the form a X plus B Y is equal to C is called a linear equation or simple equation linear equation or simple equation right for it degree is always one degree of equation is one in quadratic equation degree two in cubic equation degrees three right so degree is one but in degree degrees power power of variables let let us say x and y here are variables so power of x and y is 1 then it is a simple equation ok graph of any simple equation right graph of any simple equation or any linear equation I should write is always a straight line is always a straight line okay so you can see here how to first we'll see how to solve very simple equation or linear equation right so let's say one equation is a 1 X plus B 1 Y is equal to C 1 and other equation is a 2 X plus B 2 y is equal to C 2 now first equation I am multiplying with a B 2 second equation and multiplying it be able to solve it right how to solve linear equations just to make any terms same and subtract it right if they're all is if they're all plus signs here simply and subtracted okay so now B 1 B 2 y + B 2 B 1 I become same it can be cancelled what I left is with a 1 B 2 X minus a 2 B 1 X is equal to C 1 B 2 minus C 2 P 1 it can be written as or X is equal to C 1 B 2 minus C 2 B 1 divided by a 1 B 2 minus a 2 B 1 a 1 B 2 minus a 2 P 1 right now since this is a value of x this denominator can never be equal to 0 therefore I can write therefore I can write a 1 B 2 minus a 2 B 1 can never be equal to 0 right it means that a 1 by a 2 is not it cannot be equal to B 1 by V 2 very important point right this is the condition because if you solve like this we'll get what we will get one value of x and similarly by putting this value of x in the equation will get one value of y this is a condition for unique solution I'll get unique solution only when in two equations this is equation 1 this is equation 2 in two equations if a 1 by a 2 is not equal to B 1 by B 2 then only we will get the unique solution then only we will get the unique solution ok now the other cases are see suppose if the case of case I write 2x plus 3y is equal to 5 is one equation and 6 X + 9 y is equal to 15 is another equation right now if we try to solve it if we try to solve it by equating why I cannot solve this right because you see both x and y will get cancelled both x and y will get cancelled YX and y will create cancelled because ratio is same now see it is a 1 a 1 is 2 and B 1 is 3 ok a 2 is 6 and B 2 is 9 so you can see here a 1 by a 2 is equal to B 1 by B 2 so therefore there is a condition of what is a condition of no solution right is Krisha for unique sorry it's radicchio not a unique solution not that not a unique solution right so why because this you can see here since a 1 by a 2 is equal to B 1 by B 2 and is equal to C 1 by C 2 also because this is also 2 by 6 is 1 by 3 3 by 9 is 1 by 3 and 5 by 15 is also 1 by 3 right so is equal to C 1 by C 2 also okay so if it is true that means in this case we'll have will have infinite solutions Y will have infinite solutions here Y will have infinite solution here it is because it is because this equation 2 is nothing but a derivation from Equation 1 only see equation 1 even wait what is 3 times B n will be 2003 1 by 3 and C 1 by C 2 is also 1 by 3 right so this equation 2 is just equation 1 multiplied by 3 equation 1 multiplied by 3 will give me a question 2 that means these two are same equations this towards same equation that means we have only one equation here we don't have two equation here because a question 2 is just a question 1 multiplied by 3 so we have only one equation we have only one equation here right that is 2x plus 3 by equal to 5 we have only one equation so 2x plus 3y is equal to 5 since we have only one equation so there's no constraint on x and y so how many solution we'll keep on putting the putting the values of X and we'll keep on getting the values of Y right so in this case we have basically no solution in this case we have sorry not no solution that means infinite solution will keep we'll just we will keep on putting the value of it since we have single equation we will keep on putting the value of x and we'll keep on reading the value of y without any constraint right so that's why in finite solution okay now third one is condition for no solution see similar equation 2x plus 3y is equal to 5 and let's say 6x plus 9 Y is equal to 10 so this equation 1 this equation 2 now you can see here again we will have not will not have any unique solution because again a 1 by a 2 a 1 by a 2 is equal to B 1 by b2 so a1 by a2 is equal to v1 by v2 so it is not a case of any solution right one unique solution even by k2 should not be equal to b1 maybe - this is not a case of any solution okay fine now is this equal to c1 wasted - no because a1 by a2 and b1 maybe tour 1 by 3 this is 1 by 2 is not equal to C 1 by C 2 this is not equal to C 1 by C 2 right that means what that means what that means there this is inconsistent equations is this called inconsistent right equation is inconsistent because since a1 by a2 equal to B 1 B 2 that means it's like this is multiplied by 3 so if 2x plus 3y is equal to 5 and if it is multiplied by 3 that means 6 + 6 X + 9 Y is equal to 15 okay so 6x plus 9 Y should be equal to 15 but it is 10 only right that means in this equation this equation one gives us that 6 X + 9 y is equal to 15 but this equation is saying that 6 X + 9 y is equal to 10 so at the same time values cannot be same right at 6 s plus 9 Y cannot be 15 it is same time and 6s plus 9 Y cannot be 10 at the same time that means this is inconsistent values are inconsistent right so what is the case is the case of no solution these are case of no solution right so when you get no solution when a1 by a2 is equal to P 1 by P 2 is not equal to C 1 by C 2 okay is not equal to C 1 by C 2 correct yeah I hope it is fine okay now 3x plus py is equal to 17 and QX + 8 y is equal to 19 this equation 1 this equation 2 ok fine find thee number of pairs number of pairs of P and Q forward forward this equation will have no solution this equation will have no solution these I should write these two equations these equations these equations will have no solution there's a question okay this is the question now what I know for what is the condition of condition or no solution for no solution a 1 by K 2 is equal to B 1 by B 2 should not be equal to C 1 by C 2 so anyways C 1 by C 2 easier like this is a 1 this is a 2 this is B 1 this is B 2 right and is C 1 is 0 so anyways C 1 by C 2 is what 17 by 19 these are two prime numbers so any ratio a 1 by a 2 is 3 by something and it is p by a trivet is a 1 by a 2 a 3 by p sorry 3 by Q so a 1 by a 2 here is 3 by Q is equal to P by a anyway since there are 3 and 8 here anyway just cannot be equal to C 1 by C 2 alright because because it is 17 by 19 so how many searches you got here so you got okay P into Q we got as 24 so P into Q V we got as 24 so 24 means how many solutions 1 into 24 2 into 12 3 into 8 and 4 into 6 ok 4 into 6 now since we have been asked a pairs rate P and Q here so variables are given so variables are given that means it is ordered solution ordered solution rate for a solution always it is like four ordered solution is 1 1 comma 24 in twenty fourth one will be different right but see here in this case since it is P and finding numbers of papers of P and Q for which these equations will have no solution and you can write here just mention one more thing in question P and Q are integers P and Q are integers right positive and you do not give it that means have to take all the cases of positive and negative as well right so if it is 1 into twenty fours like any one where you take sy glaive it is four into six three or four values now 4 comma 6 6 comma 4 in ordered solution minus 4 comma minus 6 and minus 6 comma minus 4 okay minus 6 comma minus 4 right so one way one way writing P into Q as 24 in one way will have four pairs of ordered solution if naked teams also considered right so I can simply write here four pairs of all certain Mossad is there a total four pairs here so how much 4 into 4 that is 16 so we'll have 16 solutions for this question 16 solutions for this question okay 16 solutions this is the answer right simple condition for no solution is a 1 by a 2 is equal to B 1 by 8 is not equal to C 1 by C 2 this is 17 by 19 and here it is 3 here it is 8 so anyway these are prime numbers right they cannot be broken up so anyway this cannot be equal to 300 right C by something cannot be equal to 17 where it is so we don't need to certainty by 19 so don't need to consider that simple 3 by Q is equal to P by 8 P into Q is 24 there are 4 ways of writing one way will give me 4 solutions and Intel integral and ordered right both combined so integral in ordered four solutions so total 4 into 4 16 solutions it is answer correct okay now if concept here see finding finding suppose I write a number here or at when I do statement here a library in a library some books are kept when books are bundled when books are bonded bundled in groups of 11 okay four is left out okay four is left out and when they and when the books are bundled books are bundled in groups of nine in groups of nine let's say one is left out one is left out so how to form equation here how to form equation here so equation any found by so when books are bundled in groups of 11 for L of left out right second right lady number of books in library will be out big of the form so books are abundant in groups of eleven LS eleven right so let's say eleven eleven eleven there are X roofs so eleven into X and then for is left out so that number should be of the form eleven X plus four okay this equal to then the books are bundled in groups of nine one is left out okay so in groups of nine so let's say nine nine nine nine I get from why but this so one is left with a 9y plus one so that number with numbers of the form eleven x plus four is equal to nine y plus one you discussed so many such questions in numbers right same thing here a number when divided by eleven remainder is for SoCal even X plus four same number when divided by nine remainder is 1 so 9y plus one right what is my force such numbers I define his condition we can solve it easily we know how to solve it right we can solve it see 11 X always I can write nine y is equal to 11 X plus three right so well I told your two ways this in remainders how to find this right so when one says by finding remainder I can do pre mental cinema concept and second simply by hit interact so it says here it is equation okay I'm doing simply hit and trial only you can find a reminder also by putting X equal to whatever one is what you want is X&Y should be integers X & Y could be integers right because 1111 books I have make X bundles so there has to be an integer integral number of partners either there can't be three point five bundles right so nine y is equal to 11 X plus three now let's put where to square two three to put - so to sum hit enter a layer and check had to what the value of X I will get y equal to one so at X equal to 1 I'll get nine y equal to 14 why is not an integer at X equal to two we'll get nine y is equal to 25 again Y is not an integer at X equal to 3 we get 9 Y is equal to 36 11 into three plus 36 here you get Y as integer Y is equal to 4 that means y equal to four satisfied so either we'll put X equal to 3 or y equal to 4 in the ordinal equation and I will get 9 into 4 plus 1 37 is my number 37 is my number right now I told you numbers another way to do it we can do it like I can bring both the variables to the left side okay so let's we can write 11x minus 9 y is equal to minus 3 okay and what it told method to remove this remove the lower divisors saga among 11 and 9 9 is the lower devices how to remove lower divisor divide both sides by 9 and take the remainder divide both sides by 9 and take the remainder that means basically what so 9 by 9 remainder is 0 11 by 900 is 2 so it becomes 2 eggs so it's like 2 X by 9 will give me a remainder of what will give me a remainder of minus 3 so when you look at a matter of minus 320 by that is 9 so at 6 at 6 right - they will let it be when it is positively winter left-hand side so you also convert positively video to right-hand side right who discusses inhibitors and if you get negative 1/10 left-hand side so you also get negative the matter is left hand side right hand side right so 11 May 9 positive integer 2 so 2 X by 90 minute is 6 right why when is it minus 3 because 6x9 remainder is what it is minus 3 it is minus 3 okay so 2 is many wondrous things you can simply do here at what value of x will get amended as 6 obviously at X equal to 3 obviously at X equal to 3 so at X equal to 3 LLL get remainder at 6 that means X equal to 3 is a number which you're looking for okay okay so X is equal to 3 is a number which will satisfy this what will satisfy this because left hand side will be and right hand side will be equal so at X equal to 3 so simply we put C we got X 3 in here you got X 3 here okay so if simply put X equal to 3 here we'll get number as 37 so there are two ways of doing it first way is it internal second ways by reminder that okay always remember they have to in order in the side in complex questions the amended method works very easily we have shown this in reminders okay we have seen this in vendors okay so what anyhow the number is not now and what is the number number is 37 number is 37 okay fine number is 37 now again same thing right we discussed this earlier also it is like force number here is 37 what is the next number so next number should be illicium of divisors into K into K right that is 37 plus 11 and 9 are three divisors so LCM of 11 and 9 that is 99 37 plus 99 K that number is of the form 37 plus 99 K we discussed why also because if 99 K is added in 37 I want also have such numbers which when divided by 11 gives me a remainder of 4 so now if I divide this by 11 37 by eleven remainder is 4 and 99 where even invented is zero okay and if also I divide 37 plus 99 K if I divided by divided by 9 then $0.30 by 9 remainder is 1 okay 37 by 9 remainder is 1 okay and 99 where any wonder is 0 so again even this one only 4 plus 0 here is this for it is 1 so adding something which won't affect the event the right I want Rimini to be always divided all such numbers which 1/11 leaves a remainder of 4 so that remeasure busy form 37 plus 99 K because it is 11 Plus 9 11 and a 9 right so I want such that number here which which will give me a remainder 0 on dividing by 11 as well as 9 so that had that has to be there else in that is 99 that's why it is 30 centers 99 K okay so very important right let me move to national ID so it was like 11 X plus 4 is equal to is equal to 9 y plus 1 okay this equal to and this is equal to 37 plus 99 K that numbers of the form 37 plus 99 K okay now is a pattern you see is a pattern here 11 X plus 4 is equal to 9 y plus 1 okay this is a pattern here what is a pattern here pattern here is we got at X equal to okay first value positive value of x is 3 so at X is equal to 3 we got Y is equal to 4 and we got number as what 37 okay that number is of the form 30s it was 99 K so that means number will every time increase by 99 the second number will be what at k equal to 1 that is 136 what is next number 235 which at keep on adding 99 alloted all those numbers which when divided by 11 gives a remainder of 4 which 1/9 gives a remainder of 1 that is 335 sorry not 236 here to 35 and then 334 and so on now what about x and y so you see here X is equal to 3 ok so now the next value of x which will get here is directly you can write x will form an AP okay let me form right here right series of X series of X we'll be will be an AP and a B width with common difference as coefficient of Y right very important that means after X so we could buy hit and trial you got X equal to 3 now we don't need to do it at any hit enter I write after a sequel to 3 the next number satisfying our condition the next number satisfying organization at that means by putting X has some integral value I should get why you're such an integral integral value right that will be X will form in AP with common difference of coefficient of Y that is 9 so X will increase with 9 9 that means after 312 is the number which if I put here will get will get coefficient ability to I is an integer I didn't check here but in between 3 to 12 we don't want to get any number similarly for y we see if X 0 12 so 11 to 12 plus 4 136 minus 1 135 so 9 y is 135 so Y is 15 you see Y is 15 a difference in Y after 4 it is 15 what a difference in Y 11 what is 11 coefficient of x so another important point and series of Y series of Y will be an EP will be an AP with common difference as coefficient of X it's very important point very important these two points okay so X is equal to that means three and twelve and by putting X equal three by twelve you get y equal to 15 and what is the number you got if you put X 12 with a number number with one 136 correct fine now next number after 312 you add further you for add further nine so what is 3 plus 12 plus 9 again 3 plus 9 is 12 again for that nine it's an AP right it is an AP now 3 is 12 plus 9 21 what is 15 plus now it is 11 right it is 11 now what is 15 plus 11 26 okay so at 5 between 21 and 26 here by putting X has 21 or Y is 26 what is the number number lead to 35 you can see 21 into an interest for 235 so it goes like this it goes like this okay bye XS 21 26 to 35 so very point point in a two variable equation if it is if the series is like this right X will increase in a code X will increase with a coefficient of Y as the common difference in an AP and Y will increase as a coefficient of x in an AP with common difference rate as coefficient of X so Y will increase with a Y will be in AP score values of Y will be in AP with common differences coefficient of x values of X will be in AP which common differences coefficient of Y that is 9 I can write history this series here I can write this X as 3 plus 9 K 3 plus 9 K series I can write Y as 4 plus 11 K series because starting from for difference of 11 Evelynn 11 here starting from 3 difference of 9 9 so 9 K and number is of the form number is of the form 37 plus 99 K 30 Center is not a creates three important things we got here okay so we'll continue the signature video okay thank you [Music]

[Music] [Music] hi everyone today we&#39;re starting with simple equation and my name is Ravi Prakash okay simple equation is a very important topic in algebra and in this quant write the simple equation does not mean only forming equations we will discuss lots of things is simple equation right let me tell you whatever things we&#39;ll discuss in simple equation okay so in simple equation first thing we&#39;ll discuss is condition for unique solution condition for unique solution and no solution okay second thing we&#39;ll discuss is forming equations forming equations okay third thing we&#39;ll discuss is reciprocal equations reciprocal equations fourth thing we&#39;ll discuss is discuss as problems on digits right and then we will discuss it through lots of questions lots of questions right also we&#39;ll discuss this three equations and two variables cases three equations and two variables cases right so these main things we&#39;ll discuss in simple equations with lots of questions so this very important topic I&#39;ll discuss maybe some people teases in a number system or some in some depth look you&#39;ll find this in other chapters right but all these topics are related related to forming equations and solving the equation right so we keep it in this simple simple equation and a simple equation right so now let&#39;s start simple equation now see here any equation of the form a X plus B Y is equal to C is called a linear equation or simple equation linear equation or simple equation right for it degree is always one degree of equation is one in quadratic equation degree two in cubic equation degrees three right so degree is one but in degree degrees power power of variables let let us say x and y here are variables so power of x and y is 1 then it is a simple equation ok graph of any simple equation right graph of any simple equation or any linear equation I should write is always a straight line is always a straight line okay so you can see here how to first we&#39;ll see how to solve very simple equation or linear equation right so let&#39;s say one equation is a 1 X plus B 1 Y is equal to C 1 and other equation is a 2 X plus B 2 y is equal to C 2 now first equation I am multiplying with a B 2 second equation and multiplying it be able to solve it right how to solve linear equations just to make any terms same and subtract it right if they&#39;re all is if they&#39;re all plus signs here simply and subtracted okay so now B 1 B 2 y + B 2 B 1 I become same it can be cancelled what I left is with a 1 B 2 X minus a 2 B 1 X is equal to C 1 B 2 minus C 2 P 1 it can be written as or X is equal to C 1 B 2 minus C 2 B 1 divided by a 1 B 2 minus a 2 B 1 a 1 B 2 minus a 2 P 1 right now since this is a value of x this denominator can never be equal to 0 therefore I can write therefore I can write a 1 B 2 minus a 2 B 1 can never be equal to 0 right it means that a 1 by a 2 is not it cannot be equal to B 1 by V 2 very important point right this is the condition because if you solve like this we&#39;ll get what we will get one value of x and similarly by putting this value of x in the equation will get one value of y this is a condition for unique solution I&#39;ll get unique solution only when in two equations this is equation 1 this is equation 2 in two equations if a 1 by a 2 is not equal to B 1 by B 2 then only we will get the unique solution then only we will get the unique solution ok now the other cases are see suppose if the case of case I write 2x plus 3y is equal to 5 is one equation and 6 X + 9 y is equal to 15 is another equation right now if we try to solve it if we try to solve it by equating why I cannot solve this right because you see both x and y will get cancelled both x and y will get cancelled YX and y will create cancelled because ratio is same now see it is a 1 a 1 is 2 and B 1 is 3 ok a 2 is 6 and B 2 is 9 so you can see here a 1 by a 2 is equal to B 1 by B 2 so therefore there is a condition of what is a condition of no solution right is Krisha for unique sorry it&#39;s radicchio not a unique solution not that not a unique solution right so why because this you can see here since a 1 by a 2 is equal to B 1 by B 2 and is equal to C 1 by C 2 also because this is also 2 by 6 is 1 by 3 3 by 9 is 1 by 3 and 5 by 15 is also 1 by 3 right so is equal to C 1 by C 2 also okay so if it is true that means in this case we&#39;ll have will have infinite solutions Y will have infinite solutions here Y will have infinite solution here it is because it is because this equation 2 is nothing but a derivation from Equation 1 only see equation 1 even wait what is 3 times B n will be 2003 1 by 3 and C 1 by C 2 is also 1 by 3 right so this equation 2 is just equation 1 multiplied by 3 equation 1 multiplied by 3 will give me a question 2 that means these two are same equations this towards same equation that means we have only one equation here we don&#39;t have two equation here because a question 2 is just a question 1 multiplied by 3 so we have only one equation we have only one equation here right that is 2x plus 3 by equal to 5 we have only one equation so 2x plus 3y is equal to 5 since we have only one equation so there&#39;s no constraint on x and y so how many solution we&#39;ll keep on putting the putting the values of X and we&#39;ll keep on getting the values of Y right so in this case we have basically no solution in this case we have sorry not no solution that means infinite solution will keep we&#39;ll just we will keep on putting the value of it since we have single equation we will keep on putting the value of x and we&#39;ll keep on reading the value of y without any constraint right so that&#39;s why in finite solution okay now third one is condition for no solution see similar equation 2x plus 3y is equal to 5 and let&#39;s say 6x plus 9 Y is equal to 10 so this equation 1 this equation 2 now you can see here again we will have not will not have any unique solution because again a 1 by a 2 a 1 by a 2 is equal to B 1 by b2 so a1 by a2 is equal to v1 by v2 so it is not a case of any solution right one unique solution even by k2 should not be equal to b1 maybe - this is not a case of any solution okay fine now is this equal to c1 wasted - no because a1 by a2 and b1 maybe tour 1 by 3 this is 1 by 2 is not equal to C 1 by C 2 this is not equal to C 1 by C 2 right that means what that means what that means there this is inconsistent equations is this called inconsistent right equation is inconsistent because since a1 by a2 equal to B 1 B 2 that means it&#39;s like this is multiplied by 3 so if 2x plus 3y is equal to 5 and if it is multiplied by 3 that means 6 + 6 X + 9 Y is equal to 15 okay so 6x plus 9 Y should be equal to 15 but it is 10 only right that means in this equation this equation one gives us that 6 X + 9 y is equal to 15 but this equation is saying that 6 X + 9 y is equal to 10 so at the same time values cannot be same right at 6 s plus 9 Y cannot be 15 it is same time and 6s plus 9 Y cannot be 10 at the same time that means this is inconsistent values are inconsistent right so what is the case is the case of no solution these are case of no solution right so when you get no solution when a1 by a2 is equal to P 1 by P 2 is not equal to C 1 by C 2 okay is not equal to C 1 by C 2 correct yeah I hope it is fine okay now 3x plus py is equal to 17 and QX + 8 y is equal to 19 this equation 1 this equation 2 ok fine find thee number of pairs number of pairs of P and Q forward forward this equation will have no solution this equation will have no solution these I should write these two equations these equations these equations will have no solution there&#39;s a question okay this is the question now what I know for what is the condition of condition or no solution for no solution a 1 by K 2 is equal to B 1 by B 2 should not be equal to C 1 by C 2 so anyways C 1 by C 2 easier like this is a 1 this is a 2 this is B 1 this is B 2 right and is C 1 is 0 so anyways C 1 by C 2 is what 17 by 19 these are two prime numbers so any ratio a 1 by a 2 is 3 by something and it is p by a trivet is a 1 by a 2 a 3 by p sorry 3 by Q so a 1 by a 2 here is 3 by Q is equal to P by a anyway since there are 3 and 8 here anyway just cannot be equal to C 1 by C 2 alright because because it is 17 by 19 so how many searches you got here so you got okay P into Q we got as 24 so P into Q V we got as 24 so 24 means how many solutions 1 into 24 2 into 12 3 into 8 and 4 into 6 ok 4 into 6 now since we have been asked a pairs rate P and Q here so variables are given so variables are given that means it is ordered solution ordered solution rate for a solution always it is like four ordered solution is 1 1 comma 24 in twenty fourth one will be different right but see here in this case since it is P and finding numbers of papers of P and Q for which these equations will have no solution and you can write here just mention one more thing in question P and Q are integers P and Q are integers right positive and you do not give it that means have to take all the cases of positive and negative as well right so if it is 1 into twenty fours like any one where you take sy glaive it is four into six three or four values now 4 comma 6 6 comma 4 in ordered solution minus 4 comma minus 6 and minus 6 comma minus 4 okay minus 6 comma minus 4 right so one way one way writing P into Q as 24 in one way will have four pairs of ordered solution if naked teams also considered right so I can simply write here four pairs of all certain Mossad is there a total four pairs here so how much 4 into 4 that is 16 so we&#39;ll have 16 solutions for this question 16 solutions for this question okay 16 solutions this is the answer right simple condition for no solution is a 1 by a 2 is equal to B 1 by 8 is not equal to C 1 by C 2 this is 17 by 19 and here it is 3 here it is 8 so anyway these are prime numbers right they cannot be broken up so anyway this cannot be equal to 300 right C by something cannot be equal to 17 where it is so we don&#39;t need to certainty by 19 so don&#39;t need to consider that simple 3 by Q is equal to P by 8 P into Q is 24 there are 4 ways of writing one way will give me 4 solutions and Intel integral and ordered right both combined so integral in ordered four solutions so total 4 into 4 16 solutions it is answer correct okay now if concept here see finding finding suppose I write a number here or at when I do statement here a library in a library some books are kept when books are bundled when books are bonded bundled in groups of 11 okay four is left out okay four is left out and when they and when the books are bundled books are bundled in groups of nine in groups of nine let&#39;s say one is left out one is left out so how to form equation here how to form equation here so equation any found by so when books are bundled in groups of 11 for L of left out right second right lady number of books in library will be out big of the form so books are abundant in groups of eleven LS eleven right so let&#39;s say eleven eleven eleven there are X roofs so eleven into X and then for is left out so that number should be of the form eleven X plus four okay this equal to then the books are bundled in groups of nine one is left out okay so in groups of nine so let&#39;s say nine nine nine nine I get from why but this so one is left with a 9y plus one so that number with numbers of the form eleven x plus four is equal to nine y plus one you discussed so many such questions in numbers right same thing here a number when divided by eleven remainder is for SoCal even X plus four same number when divided by nine remainder is 1 so 9y plus one right what is my force such numbers I define his condition we can solve it easily we know how to solve it right we can solve it see 11 X always I can write nine y is equal to 11 X plus three right so well I told your two ways this in remainders how to find this right so when one says by finding remainder I can do pre mental cinema concept and second simply by hit interact so it says here it is equation okay I&#39;m doing simply hit and trial only you can find a reminder also by putting X equal to whatever one is what you want is X&amp;Y should be integers X &amp; Y could be integers right because 1111 books I have make X bundles so there has to be an integer integral number of partners either there can&#39;t be three point five bundles right so nine y is equal to 11 X plus three now let&#39;s put where to square two three to put - so to sum hit enter a layer and check had to what the value of X I will get y equal to one so at X equal to 1 I&#39;ll get nine y equal to 14 why is not an integer at X equal to two we&#39;ll get nine y is equal to 25 again Y is not an integer at X equal to 3 we get 9 Y is equal to 36 11 into three plus 36 here you get Y as integer Y is equal to 4 that means y equal to four satisfied so either we&#39;ll put X equal to 3 or y equal to 4 in the ordinal equation and I will get 9 into 4 plus 1 37 is my number 37 is my number right now I told you numbers another way to do it we can do it like I can bring both the variables to the left side okay so let&#39;s we can write 11x minus 9 y is equal to minus 3 okay and what it told method to remove this remove the lower divisors saga among 11 and 9 9 is the lower devices how to remove lower divisor divide both sides by 9 and take the remainder divide both sides by 9 and take the remainder that means basically what so 9 by 9 remainder is 0 11 by 900 is 2 so it becomes 2 eggs so it&#39;s like 2 X by 9 will give me a remainder of what will give me a remainder of minus 3 so when you look at a matter of minus 320 by that is 9 so at 6 at 6 right - they will let it be when it is positively winter left-hand side so you also convert positively video to right-hand side right who discusses inhibitors and if you get negative 1/10 left-hand side so you also get negative the matter is left hand side right hand side right so 11 May 9 positive integer 2 so 2 X by 90 minute is 6 right why when is it minus 3 because 6x9 remainder is what it is minus 3 it is minus 3 okay so 2 is many wondrous things you can simply do here at what value of x will get amended as 6 obviously at X equal to 3 obviously at X equal to 3 so at X equal to 3 LLL get remainder at 6 that means X equal to 3 is a number which you&#39;re looking for okay okay so X is equal to 3 is a number which will satisfy this what will satisfy this because left hand side will be and right hand side will be equal so at X equal to 3 so simply we put C we got X 3 in here you got X 3 here okay so if simply put X equal to 3 here we&#39;ll get number as 37 so there are two ways of doing it first way is it internal second ways by reminder that okay always remember they have to in order in the side in complex questions the amended method works very easily we have shown this in reminders okay we have seen this in vendors okay so what anyhow the number is not now and what is the number number is 37 number is 37 okay fine number is 37 now again same thing right we discussed this earlier also it is like force number here is 37 what is the next number so next number should be illicium of divisors into K into K right that is 37 plus 11 and 9 are three divisors so LCM of 11 and 9 that is 99 37 plus 99 K that number is of the form 37 plus 99 K we discussed why also because if 99 K is added in 37 I want also have such numbers which when divided by 11 gives me a remainder of 4 so now if I divide this by 11 37 by eleven remainder is 4 and 99 where even invented is zero okay and if also I divide 37 plus 99 K if I divided by divided by 9 then $0.30 by 9 remainder is 1 okay 37 by 9 remainder is 1 okay and 99 where any wonder is 0 so again even this one only 4 plus 0 here is this for it is 1 so adding something which won&#39;t affect the event the right I want Rimini to be always divided all such numbers which 1/11 leaves a remainder of 4 so that remeasure busy form 37 plus 99 K because it is 11 Plus 9 11 and a 9 right so I want such that number here which which will give me a remainder 0 on dividing by 11 as well as 9 so that had that has to be there else in that is 99 that&#39;s why it is 30 centers 99 K okay so very important right let me move to national ID so it was like 11 X plus 4 is equal to is equal to 9 y plus 1 okay this equal to and this is equal to 37 plus 99 K that numbers of the form 37 plus 99 K okay now is a pattern you see is a pattern here 11 X plus 4 is equal to 9 y plus 1 okay this is a pattern here what is a pattern here pattern here is we got at X equal to okay first value positive value of x is 3 so at X is equal to 3 we got Y is equal to 4 and we got number as what 37 okay that number is of the form 30s it was 99 K so that means number will every time increase by 99 the second number will be what at k equal to 1 that is 136 what is next number 235 which at keep on adding 99 alloted all those numbers which when divided by 11 gives a remainder of 4 which 1/9 gives a remainder of 1 that is 335 sorry not 236 here to 35 and then 334 and so on now what about x and y so you see here X is equal to 3 ok so now the next value of x which will get here is directly you can write x will form an AP okay let me form right here right series of X series of X we&#39;ll be will be an AP and a B width with common difference as coefficient of Y right very important that means after X so we could buy hit and trial you got X equal to 3 now we don&#39;t need to do it at any hit enter I write after a sequel to 3 the next number satisfying our condition the next number satisfying organization at that means by putting X has some integral value I should get why you&#39;re such an integral integral value right that will be X will form in AP with common difference of coefficient of Y that is 9 so X will increase with 9 9 that means after 312 is the number which if I put here will get will get coefficient ability to I is an integer I didn&#39;t check here but in between 3 to 12 we don&#39;t want to get any number similarly for y we see if X 0 12 so 11 to 12 plus 4 136 minus 1 135 so 9 y is 135 so Y is 15 you see Y is 15 a difference in Y after 4 it is 15 what a difference in Y 11 what is 11 coefficient of x so another important point and series of Y series of Y will be an EP will be an AP with common difference as coefficient of X it&#39;s very important point very important these two points okay so X is equal to that means three and twelve and by putting X equal three by twelve you get y equal to 15 and what is the number you got if you put X 12 with a number number with one 136 correct fine now next number after 312 you add further you for add further nine so what is 3 plus 12 plus 9 again 3 plus 9 is 12 again for that nine it&#39;s an AP right it is an AP now 3 is 12 plus 9 21 what is 15 plus now it is 11 right it is 11 now what is 15 plus 11 26 okay so at 5 between 21 and 26 here by putting X has 21 or Y is 26 what is the number number lead to 35 you can see 21 into an interest for 235 so it goes like this it goes like this okay bye XS 21 26 to 35 so very point point in a two variable equation if it is if the series is like this right X will increase in a code X will increase with a coefficient of Y as the common difference in an AP and Y will increase as a coefficient of x in an AP with common difference rate as coefficient of X so Y will increase with a Y will be in AP score values of Y will be in AP with common differences coefficient of x values of X will be in AP which common differences coefficient of Y that is 9 I can write history this series here I can write this X as 3 plus 9 K 3 plus 9 K series I can write Y as 4 plus 11 K series because starting from for difference of 11 Evelynn 11 here starting from 3 difference of 9 9 so 9 K and number is of the form number is of the form 37 plus 99 K 30 Center is not a creates three important things we got here okay so we&#39;ll continue the signature video okay thank you [Music]

Transcript for:Understanding Simple Equations in Algebra

Transcript for:
Understanding Simple Equations in Algebra