Dear learners, now we shall discuss about linear equations. When two expressions are separated by an equality sign, it is called an equation. The equality sign shows that the expression to the left of the sign is equal to the expression to the right of the sign. For example, 5 plus 2 equal to 7. Some equations contain unknown numbers which are usually represented by letters of English alphabets. We most often use the letters x and y and these letters are known as variables or unknowns.
A number on its own is called a constant. A coefficient is a number used to multiply a variable. For example, 6x means 6 times x. Here 6 is a coefficient of x.
Standard form of a linear equation in one variable. A linear equation in one variable is an equation that can be written in the form x. plus b equal to c where a b and c are real numbers and a is non-zero. For example 3x plus 4 equal to 13. In linear equations exponent on the variable is always 1 a value such that when we replace the variable with it it makes the equation true is known as its solution.
x equal to 4 is a solution of the linear equation. x plus 5 equal to 9 because 4 plus 5 equal to 9 is true. For solving a linear equation, we are to get the variable alone on one side and everything else on the other side. Let us take a linear equation and find its solution.
Equation is 2x plus 3 equal to 11. We know that if two expressions are equal and we add or subtract the same constant to both sides, two sides will remain equal. 2x plus 3 equal to 11 implies 2x equal to 11 minus 3. We also know that if two expressions are equal and we multiply or divide except for 0 the same constant to both the sides the two sides will remain equal. 2x equal to 11 minus 3 equal to 8 implies x equal to 8 divided by 2. 2 equal to 4. Therefore, x equal to 4 is the solution of the linear equation 2x plus 3 equal to 11. Let us consider another linear equation x equal to x plus 2. For solving a linear equation, we want to get the variable on one side and everything else on the other side. We know that if we add or subtract the same thing to both the sides, the two sides remain equal.
x minus x equal to 2 implies 0 equal to 2 which is not true. Variable has disappeared. Therefore, linear equation x equal to x plus 2 has no solution. Let us consider another linear equation. 2x plus 4 equal to x plus 4 plus x.
For solving this equation, let us take the variable x on one side and everything else on the other side. By doing so, we get 0 equal to 0, which is always true. Therefore, linear equation 2x plus 4 equal to x plus 4 plus x has infinitely many solutions. We have seen that a linear equation in one variable may have one solution, infinitely many solutions or no solution.
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