Check graphically whether the pair of equations
$x+3y=6$ $...(1)$
and $2x-3y=12$ $...(2)$
is consistent. If so,solve them graphically.

(N/A) Let us draw the graphs of the Equations $(1)$ and $(2).$ For this,we find two solutions for each of the equations,which are given in the tables below:
For Equation $(1): x+3y=6$

$x$	$0$	$6$
$y = \frac{6-x}{3}$	$2$	$0$

For Equation $(2): 2x-3y=12$

$x$	$0$	$3$
$y = \frac{2x-12}{3}$	$-4$	$-2$

Plot the points $A(0, 2), B(6, 0)$ for line $(1)$ and $P(0, -4), Q(3, -2)$ for line $(2)$ on graph paper. Join the points to form the lines $AB$ and $PQ$.
We observe that there is a point $B(6, 0)$ common to both the lines $AB$ and $PQ.$ Since the lines intersect at a point,the pair of linear equations is consistent. The solution is $x=6$ and $y=0.$