Let us solve the simultaneous equations 2x + y = 8 and 2y – 3x = –5 by the method of comparison and justify them by solving graphically.

expressing the equations in terms of one variable.

2x + y = 8

………[1]

2y – 3x = –5

⇒ 3x = 2y + 5

………[2]

by comparing eq. [1] and eq. [2]

⇒24 – 3y = 4y + 10

⇒7y = 14

⇒ y = 2 ………[3]

by using [3] in [1]

Let’s make the graphs of given linear equations,

We get the following tables for the given linear equations.

For 2x + y = 8

y = 8 – 2x

For 2y - 3x = - 5

Plotting these points on a graph and joining them, we get two straight lines.

From the graph, we can see that both lines intersect at (3, 2), hence the solution to this pair is (3, 2).