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

8x + 5y – 11 = 0

3x – 4y – 10 = 0

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

8x + 5y = 11 (i)

3x – 4y = 10 (ii)

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

Note: - We can eliminate any one of the variable, to eliminate y, we have to make the coefficient of y in both the equations equal.

We have to multiply the coefficient of y with such a number that makes them equal to the common factor of both of them.

Multiply equations (i) with 4 and (ii) with 5 .

⇒ x = 2, putting the value of x = 2 in equation (i), we get y = - 1

Hence the solution of the two 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 8x + 5y = 11

For 3x – 4y = 10

Hence also by graphical method the solution comes out to be (2, - 1)