all right uh last example that we're going to go over um ladies and gentlemen now what we're going to be talking about is a systems of inequalities and today that's basically it's basically what our lesson is about even though as you guys can see that this is going to be very similar to what we have done uh you know what i previously did and what we've done in the last class period it's just really an extension so that's why we're not going to spend the whole day just working on these but we're just going to incorporate it in with the rest of the lesson so in this example now i have two inequalities that i have and basically what we're going to be doing is we're going to be graphing the system where they um are going to intersect or graph the solution where they're going to intersect so the first thing i want to do is make sure that i can graph these in their slope intercept form so this one i'm going to rewrite as x plus y is less than 4 and to go ahead and graph this i'm going to want to write this in slope intercept form so i'll subtract an x so i have y is less than negative x plus 4. now remember when graphing with a negative 1 as your slope when you have a negative x right remember we we need to have a number we need to have a fraction as our slope so our coefficient you have the negative remember we can always write in that's a negative 1. that doesn't change the problem negative 1 times x is just negative x but again remember i said i always want to have it as a fraction so i'm going to write this over posi over 1 because negative 1 divided by 1 is the same thing as just negative 1. but when i'm computing my slope i like to leave i like to be able to use fractions with that so now let's go ahead and graph it so the first thing we do is plot the y-intercept because i think that's the easiest thing to do the y-intercept remember is going to be your constant so i go up positive 4 on the y-axis 1 2 3 4 and i make a nice big dot then i use my slope which says the change in the y-coordinates is 1 negative 1 and the change in the x coordinates is positive 1. so since the change in the y coordinates is negative 1 i'm going to go down since the change in the x coordinates is positive 1 i go to the right then i look at my inequality symbol and i notice that it is less than so it's going to be a dashed line and then the last thing i'm going to do is use shading so i'll pick 0 0 or i test i'll pick 0 0 and i'll just plug in 0 in for x and 4 y and i get 0 is less than 4 which is true so since that is true i am going to shade below however when i have a system of two inequalities rather than graphing all the lines i just like to use arrows for this just so i can i'm not always creating like too much work i know i'm going to shade down below the low the uh line in this case now we go ahead and graph this one well this one's already in slope intercept form so it's a little bit easier again notice that my slope as a fraction that can be rewritten as one over one so now my y intercept's negative three so i go down negative three one two three and then my slope now is going to be up 1 over 1 and since it's greater than or equal to that's going to be a solid line and then i use a test point to determine um if my test point is going to be true or false so i have 0 is greater than or equal to 0 minus 3 and that is end up going to be true again so since that is true i shade above and then you guys can see that the only region where both of my inequalities are true is right here okay and that's it so when you're doing a system of inequalities all you guys are basically doing is just graphing two of them on the same