9x+2y=39
6x+13y = -9
multiply the first by 2 and the second by 3
18x + 4y = 78
18x + 39y = -27
Subtract the second from the first
4y - 39y = 78 - -27
-35y = 78 + 27
-35y = 105
Divide both sides by - 35
y = -3
substituting into the second equation
6x + 13(-3) = -9
6x - 39 = -9
collect like terms
6x = -9 + 39
6x = 30
Divide both sides by 6
x = 5
Hence
(x,y) = (5, -3)