i would solve this problem by substitution method
as it would take a lot longer to use any other method
-11x-10y=17
lets find x
5x-7y=50
5x=7y+50
x=7/5 y +10
we will substitute our x in the first eq
-11(7/5 y+10)-10y=17
-77/5 y-110 -10y=17
we solve this equation and we get y=-5
so if we have y=-5
5x-7(-5)=50
5x+35=50
5x=50-35
5x=15
x=3
y=-5