We draw the graphs of given linear equations as follows :
x + 3y = 6
⇒ 3y = 6 – x
⇒ y = 6−x/3
We put the different values of x in this equation then we get different values of y and we prepare the table of x, y for equation x + 3y = 6
and 2x – 3y = 12
⇒ 3y = 2x – 12
⇒ y = 2x−12/3
We put the different values of x in this equation then we get the different values of y and we prepare the table of x, y for equation 2x – 3y = 12.
Now, we plot the points (0, 2), (3, 1) and (6, 0) on the graph paper and we draw a graph passing through these points.
We get a graph of linear equation x + 3y = 6, again we plot the points (0, – 4), (3, – 2) and (6, 0) on the graph paper and we draw a graph passing through these points again we get a graph of linear equation 2x – 3y = 12. We observe that graphs of equations x + 3y = 6 and 2x – 3y – 12 intersect each other at point (6, 0). Hence, x = 6, y = 0 is the solution of given equations. Therefore, given pair of equations is consistent.
