Solve the system of equations

 x+y=0

 8x - 7y = 75

Rearranging the first equation produces  x = - y

Subbing this for x in the second equation, we have

8(-y) -  7y = 75

-8y- 7y  = 75

-15y  = 75    divide both sides by -15

y = -5

And x = -y   so x   = -(-5)  = 5

So  {x, y}   = {5, -5}