The best way to do this equation would be subtraction
-11x-10y=17
5x-7y=50
multiply the top equation by -7 and the bottom equation by 10
77x+70y=-119
50x-70y=500
The y cancels out
127x=381
x=3
plug y back into the original equation
-11(3)-10y=17
-33-10y=17
-10y=50
y=-5
(3,-5)