Solve the following pair of linear equation in two variables (by graph)

x–y = 6, 3x – 3y = 18

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 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

x—y = 6

for, 3x—3y = 18

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

From the graph, we can see that both lines coincide and hence there are infinite number of solutions.