## Chapter: 3

## What Are Linear Equations in Two Variables ?

## Linear Equation In Two Variables

• An equation of the form ax + by + c = 0, where a, b, c are real numbers, such that a and b together cannot be zero, is called a linear equation in two variables.

• A linear equation in one variable can also be written as linear equation in two variables by taking coefficient of other variable as zero.

## Solution Of Linear Equation In Two Variables

• The values of variables which satisfied the given linear equation are called the solutions.

• A linear equation in two variables has infinitely many solutions.

• The solution of a linear equation is not affected when

(i) the same number is added to (or subtracted from) both sides of the equation.

(ii) both sides of the equation are multiplied (or divided) by the same non-zero number.

## Some Important Facts

• x = 0 is the equation of the y – axis and y = 0 is the equation of the x – axis.

• x = a represents a straight line parallel to y – axis and y = a represents a straight line parallel to x – axis.

• y = mx represents a straight line passing through the origin.