how do i solve this equation?

5x+2y=-15
3x-y=2

-y=2-3x
y=-2+3x

5x+2(-2+3x)=-15
5x-4+6x=-15
11x=-15+4
11x=-11
x=-1 answer//

plug in x=-1 to y=-2+3x

y=-2+3(-1)
y=-2-3
y=-5 answer//

Modify the equation 3x-y=2 by adding y to both sides. you now get
3x-y+y =2+y the -y+y on the left cancel each other out leaving you with. 3x=2+y
Divide both sides by 3 giving you 3x/3=(2+y)/3

the 3 above and below on the left leaving you with x= (2+y)/3
Now substitute this equation into the 5x+2y=-15
Giving 5((2+y)/3)+2y=-15

Now simplify on the left : (10+5y)/3+2y=-15
Simplify again on the left: 10/3 + 5y/3+2y=-15
and again: 10/3+11y/3=-15
and again: 10+11y=-45
and again: 11y=-55
and finally: y=-55/11=-5

Now go back and substiute the y in the equation 3x-y=2
giving you 3x-(-5)=2
Simplify: 3x+5=2
Giving 3x=-3
Finally x=-1

So the solution is x=-1 y=-5

That was a bit messy but we got there!

5x + 2y = -15
3x - y = 2

3x - y = 2
y = (3x - 2) ...... (1)

5x + 2y = -15

Substitute (1) for y.
5x + 2(3x - 2) = -15
5x + 2(3x) - 2(2) = -15
5x + 6x - 4 = -15
11x = -15 + 4
x = -11/11
x = -1

3x - y = 2

Substitute -1 for x.
3(-1) - y = 2
-3 - y = 2
y = -3 - 2
y = -5

∴ x = -1, y = -5

You solve it using the substitution method, with your working so that your teacher can check you actually understood what you were doing, and help you if you didn't.

The substitution method is really useful. I've linked you to some websites that explain how to use this method. You really need to understand the basic method, then have a go at the question yourself. So, check out the links, see which works best for you, then have a go at your question.

When you've had a go, edit your question to add your answer and I'll let you know if you got it right :)

y = 3x - 2
sub in 1st eqn,
5x + 2(3x-2) =-15
5x+6x-4=-15
11x=-11
x=-1

First, you need to solve one of the equations for either x or y.
Solving the second equation for y will give you
y = 3x - 2

Then, substitute 3x - 2 for y in the first equation, to get
5x + 2(3x - 2) = -15

5x + 6x - 4 = -15

11x = -11

x = -1

Then, you can use x to solve for y in either equation. Using the second equation, we would get
3(-1) - y = 2

y = -3 - 2

y = -5

You solve for x or y with one of the equations. You then substitute that into the other equation and you should get the answer for one of the variables. You then substitue that variable and get the answer for the other variable.