Question

Show graphically that each of the following given systems of equations has infinitely many solutions:

$x-2y=5,3x-6y=15.$

Answer 1

So we have

x - 2y = 5 and 3x - 6y = 15

Now, x - 2y = 5

=> x = 2y + 5

When y = -1 then, x = 3

When y = 0 then, x = 5

Thus, we have the following table giving points on the line x-2y=5

X	3	5
Y	-1	0

Now, 3x-6y=15

=> $x=\frac{(15+6y)}{3}$

When y=-1, then x=3

When y=0, then x= 5

Thus, we have the following table giving points on the line 3x-6y=15

X	3	5
Y	-1	0

Thus the graphs of the two equations are coincident.

Hence, the system of equations has infinitely many solutions.