In this case, you have to use substitution.

Lets name the two equations A and B for now. Use equation A first

4x - 5y = - 18

Isolate either y or x. I'll use x.
...

In this case, you have to use substitution.

Lets name the two equations A and B for now. Use equation A first

4x - 5y = - 18

Isolate either y or x. I'll use x.

4x = 18 + 5y
x = (18+5y/4) [The 4 is over "18 + 5y)]

Now put this value of x in equation B

5x + 4y = -2
5(18 + 5y/ 4) + 4y = -2

Now you solve for the value of y. The way I'm doing it, I'll multiply each value in the equation by 4 so I can get rid of the fraction first(18 + 5y / 4)

So now you have

5(18 + 5y) + 4y = -2

Open the brackets by mutliplying

90 + 25y + 4y = -2
29y = -2 - 90 (We added up the 'y' values above and move the 90 to the other side so it becomes negative)

29y = -92
y = -92 / 29

Now plug this back into equation A and get your x value :D

We can solve this by elimination:

4x-5y=-18 ----(1)
5x+4y=-2 ---- (2)
then we can multiply (1) by 5 and multiply (2) by 4
20x-25y=-90 -- (3)
20x+16y=-8 -- (4)
...

We can solve this by elimination:

4x-5y=-18 ----(1)
5x+4y=-2 ---- (2)
then we can multiply (1) by 5 and multiply (2) by 4
20x-25y=-90 -- (3)
20x+16y=-8 -- (4)
Now, we can have (3) minus (4)
20x-25y=-90
-) 20x+16y=-8
_______________
-41y = -82
y=2

since y=2, we can substitute to any of the equations and get x
5x+4(2)=-2
5x = -2-8
5x=-10
x=-2

Therefore, x = -2, y=2