Question 245972
Here, this is actually pretty easy to understand.

5x + 5y = -11
7x - 3y = 17

Our goal is to eliminate one of the variables, I'm going to eliminate the y.

Multiply the top one by three, and the bottom one by five.

15x + 15y = -33
35x - 15y =  85

Add the equations together

50x = 52
x = 26/25

insert into orginal problem

5(26/25) + 5y = -11
5.2 + 5y = -11
5y = -16.2
y = -3.24

Check

5.2 - 16.2 = -11
Correct

I believe your algrebra II teacher will want it written as x = 5 1/5, and y = -3 6/25




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Sincerly,
      Andrew