Question

Show graphically that each of the following given systems of equations is inconsistent,i.e., has no solution:

$x-2y=6,3x-6y=0$

Answer 1

We have, $x-2y=6and3x-6y=0$

Now x-2y=6

= x= 6+2y

When y=-2 then, x=2

When y=-3 then, x=0

Thus, we have the following table giving points on the line x-2y=6

X	2	0
Y	-2	-3

Now , 3x - 6y = 0

=x = 2y

When y = 0, then y = 0

When y=-1 , then x = 2

Thus, we have the following table giving points on the line 3x - 6 y = 0

X	0	2
Y	0	1

Graph of the equation x-2y=6 and 3x-6y=0

Clearly, two lines are parallel to each other. So, the two lines have no common point.

Hence the given system has no solutions.