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

4x - 8y = 0

-3x + 8y = - 7

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)

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.