Question

show graphically that 2 X + 3 Y = 6 and 4 x + 6 Y = 12 has infinitely many solutions​

Answer 1

Answer:

Step-by-step explanation:

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

11

Thus the graphs of the two equations are coincident.

Hence, the system of equations has infinitely many solutions.