Question

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

Answer 1

The way I would do it is the following.

Multiply x+5y=-3 by 3, making it 3x+15y=-9. Now, you can subtract the one equation from the other So, if you wrote it properly, it would look like

3x+15y=-9
-(3x-2y=8)
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=>17y=-17 which means y=-1. Now you can plug in y=-1 in the first equation, x+5y=-3, showing that x-5=-3, meaning x=2.

This is how I would do it. Of course, one could also solve for x in terms of y in the first equation, solving that x=-3-5y, and then substituting that into the second equation. I hope this is helpful.

Answer 2

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