Solve the following systems of equations algebraically using elimination
-2x+4y=4
3x-4y=2

Hey there!

When solving systems of equations by elimination, what we do is we remove one variable by combining the equations and then we solve for one variable.

How does this work?

Well, let's say we have 2x in one equation and 2x in the other equation. If we combine the equations, it will simply be 4x! What we need to do is multiply one of the equations by -1, which will make one of the 2x's and -2x. Then, if we combine the two equations, our x's will be cancelled out and we can solve for y.

In this case, we don't need to change any of the equations because we have 4y in one equation and -4y in the other, so we will just add the equations and then solve for x.

-2x+4y=4

+

3x-4y=2

=

x=6

Now, we plug this into one of our equations to find y.

18-4y=2

-4y=-16

y=4

Therefore, our solution is x=6 and y=4.

I hope this helps!