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5x+8y=-19
x+6y=-17
Multiply the second equation by -5
-5(x+6y=-17)
-5x-30y=85
Add to the first equation
5x + -5x + 8y + -30y = -19 + 85
-22y = 66
y = -3
x = -17 - 6(-3)= - 17 - (-18) = 1
Proof
5(1)+8(-3)=5+-24=-19