How many solutions does this system of equations have?

y = –2x + 2
2y + 4x = 4

Step-by-step explanation:

First we solve it.

I'll use substitution.

In the first equation y equals -2x+2 so we can apply that to the second equation

2y + 4x = 4

2(-2x+2) + 4x = 4

distribute

-4x+4+4x=4

simplify

4=4

To figure out how many solutions it has:

•If both side of the equal sign are exactly the same: Infinitely many

ex: 6x=6x

•If both sides of the equal sign do not match when completely simplified: No solutions

ex: 3x=-5x

•If it creates an equation: 1 solution

ex: x=3+2y

Since both sides of the equal sign are 4, we have infinitely many solutions.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

step-by-step explanation:

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