Question

The pair of linear equations are

$2x-3y=6$
$\frac{x}{2}+\frac{y}{3}=1$

• A. Parallel
• B. Identical
• C. Perpendicular
• D. Coplanar

Answer 1

Answer: (C), (D)

To draw the graph for the given linear equation, we need to first plot the points which lie on it, join them to get a straight line.
First equation is $2x-3y=6⟹y=\frac{2}{3}x-2$
Substitute different values of x in the equation and calculate to get corresponding values of y.

$x$	$y=\frac{2}{3}x-2$	Point $(x,y)$
$0$	$-2$	$(0,-2)$
$3$	$0$	$(3,0)$
$6$	$2$	$(6,2)$
$-3$	$-4$	$(-3,-4)$
$-6$	$-6$	$(-6,-6)$

Second equation is $\frac{x}{2}+\frac{y}{3}=1⟹y=-\frac{3}{2}x+3$
Substitute different values of x in the equation and calculate to get corresponding values of y.

$x$	$y=-\frac{3}{2}x+3$	Point $(x,y)$
$0$	$3$	$(0,3)$
$2$	$0$	$(2,0)$
$4$	$-3$	$(4,-3)$
$-2$	$6$	$(-2,6)$
$-4$	$9$	$(-4,9)$

Plot these points on the graph paper and join them using a straight line.
On observing the graph, we find that the two lines intersect each other at right angle. Hence, they are perpendicular to each other.