-5x+3y = 11
3x+2y = -21
First you need to cancel out one variable so you can solve for the other, I chose x since they have opposite signs. You need to make the bottom variable of x equal to the top variable so they cancel out. You can multiply the top by 3 and the bottom by 5.
3(-5x+3y = 11)
5(3x+2y = -21)
It then becomes
-15x+9y = 33
15x+10y = -105
Now add the individual components together, for instance add -15x and 15x to get 0x and so on to get
0x+19y=-72
Now solve for y
Divide both sides by 19.
Approximately
Now plug this y value into either equation to solve for x
Multiply by 2
Add 144/19 to both sides
Find common denominator
Simplify
Approximately
So x=-255/57 and y=-72/19