How many solutions are there to the following system of equations?

4x - 8y = 0
-3x + 8y = -7

When we add the equations together, we need up with x=-7

substitute this and we get -28-8y=0 so y =-3.5

I think this is right.

we can also see the if we divide both of the answers by 3.5, x=-2 and y=-1. We can also remove the negatives of both and that will still work.

There's 3 right there for you. there may be more.

We can add the equations and cancel out the y terms
4x-8y=0
-3x+8y=-7 +
1x+0y=-7

x=-7
duh

sub back to find the x term
4x-8y=0
4(-7)-8y=0
-28-8y=0
add 8y both sides
-28=8y
divide by 8
-7/2=y

one solution, (-7,-7/2)