Let us solve the following simultaneous linear equations in two variables by the method of elimination and check them graphically:

2x + 3y – 7 = 0

3x + 2y – 8 = 0

Rewriting the above equations in the standard form of ax + by = c

2x + 3y = 7 (i)

3x + 2y = 8 (ii)

In this problem, we will eliminate ‘x’ from both the equations (i) & (ii)

Multiply equations (i) with 3 and (ii) with 2 to make the coefficient of x equal.

⇒ y = 1, Putting the value of y in equation (i) gives x = 2

Hence the solution of this linear equation is x = 2 and y = 1.

Let us take the equation (i) as Straight Line A and (ii) as B . To draw the lines we need at least 2 points to draw

Generally, we substitute x = 0 or y = 0 in the given linear equations to get y and x. So we get two points on the straight line. To find more points on the line, take different values of x related to it, we get different values for y from the equation.

We get the following tables for the given linear equations.

For 2x + 3y = 7

For 3x + 2y = 8

Hence, Also by graphical method the solution comes out to be (2, 1).