How do you solve
x+5y=-3
3x-2y=8

Use substitution.

First we want to isolate one of the variables. Here's how you'd do that.

x +5y = -3
x = -3 -5y

Now we can just substitute -3 -5y for x in the other equation and solve for y!

3x - 2y = 8
3(-3 -5y) -2y = 8
-9 -15y -2y = 8
-9 -17y = 8
17y = 17
y = 1

And then use y = 1 in an earlier equation to find x.

x + 5y = -3
x + 5*1 = -3
x + 5 = 3
x = -2