Question

What is the value of y in the solution to the following system of equations?

2x + y = -4
5x + 3y = -6

Answer 1

If we extend to first eq. with (-3) and sum to these equations we get (-x)=6 so x=-6 then
if 2x+y=-4
y=8

Answer 2

If we do this by elimination, we would multiply the top by -3, so the y-values would cancel out. That would give us
-6x-3y=12
5x+3y=-6 Now we add/cancel them and get
----------
-x=6 [Divide both sides by -1]
x=-6

Now that we know what the x-value is we will sub this back into any of the two equations and solve for y. I chose the 1st just because
2(-6)+y=-4
-12+y=-4 [Add 12 on both sides and get]
y=8

That means our solution is (-6,8)