Question

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

$2x+3y=6,4x+6y=12.$

Answer 1

So we have 2x+3y=6 and 4x+6y=12

Now, 2x+3y=5

= x= 6−3y2

When y=0 then, x=3

When y=2 then, x=0

Thus, we have the following table giving points on the line 2x+3y=6

X	0	3
Y	2	0

Now, 4x+6y=12

=x=12−6y4

When y=0, then x=3

When y=2, then x= 0

Thus, we have the following table giving points on the line 4x+6y=12

X	0	3
Y	2	0

Graph of the equation 2x+3y=6 and 4x+6y=12

Thus the graphs of the two equations are coincident.

Hence, the system of equations has infinitely many solutions.