HELP PLS +10 POINTS (SHOW WORK PLS)

Hi there!

For a system to have an infinite number of solutions, both expressions must be equal. We can go through each system and determine this:

F:

x + 2 = y

4 = 2y - x

If we rearrange so that both are in the same format, we get:

x + 2 = y

x + 4 = 2y

These cannot be equal, so they do not have infinite solutions.

G:

2y + 6 = 4x

-3 = y - 2x

Rearrange:

2y + 6 = 4x

-y - 3 = -2x

We can try to make the bottom equation look like the top equation by multiplying all terms by -2. We get:

2y + 6 = 4x. This is the same as the top, so G has infinite solutions.

Just to be sure, we can go through the others:

H:

y + 3 = 2x

4x = 2y - 3

Rearrange:

y + 3 = 2x

2y - 3 = 4x. Cannot be equal to the other equation.

J:

y = 2x - 5

y = 2x - 2. Not equal.

The correct answer is G.