A system of equations has infinitely many solutions. If 2y - 4x = 6 is one of the equations, which could be the other
equation?
y = 2x + 6
y = 4x + 6
-y=-2x - 3
y=-4x + 6
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-y = -2x - 3

Option 3

Step-by-step explanation:

When equations are equivalent, they will have infinitely many solutions.

If you want to find an equivalent equation, you can multiply/divide every term in the equation by the same number. You can also rearrange the equation.

Since the options mostly have "y" by itself, start by rearranging to isolate "y" in the given equation.

Move all the other numbers to the right of the equal sign except for "y". To move a number, apply its reverse operation to the entire equation.

Do reverse operations in reverse BEDMAS order.

2y - 4x = 6                Move "-4x" first. It's reverse is +4x.

2y - 4x + 4x = 6 + 4x

2y = 6 + 4x                Move the "2" in 2y. Divide the whole equation by 2.

2y/2 = 6/2 + 4x/2

y = 3 + 2x                  Rearrange to look like the answer choices.

y = 2x + 3

This equation looks like option 3 except every term has a different negative/positive.

y = 2x + 3         -y = -2x - 3

We can multiply every term by -1.

y = 2x + 3

y*-1 = 2x*-1 + 3*-1

-y = -2x + (-3)                Negative and positive make a negative

-y = -2x - 3                     Same as option 3

step-by-step explanation: