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8x - 3y = -11
2x - 5y = 27
let us multiply the second equation by 4 and subtract it from the first, thus eliminating the x's...
8x - 3y = -11
-(8x - 20y = 108)
and we get
17y = -119
y = -7
and then by substituting we get
2x - 5(-7) = 27
2x + 35 = 27
2x = -8
x = -4