Question

Solve the system using elimination.
{2x+6y=-12
{5x-5y=10

Answer 1

You say we have:
{2x+6y=-12
{5x-5y=10
Okay, what we need to do, in order to elimiate either x or y, would be multiplying any of those two ecuations by a number, so we have two opposites.
I'll multiply the first one by -5 and the second one by 2.
We'll end up having:
{-10x-30y=-60
{10x-10y=20
So we can simplify the Xs and sum the ecuations with only y on them.
{-30y=-60
{-10y=20
We'll end up having:
-40y=-40 => y=-40/-40 => y=1
Now we know that y01, you just take one of the other initial ecuations and replace it.

So, we have for example:
2x+6y=-12 ; y=1 => 2x+6(1)=-12
We'll end up having:
2x=-18
then:
x= -18/2
x=-9.

And all you have to do is veify if the solutions are correct :)