multiply second equation by -1 and add to 2nd equation
5x+8y=77
-5x-6y=-65 +
0x+2y=12
2y=12
divide both sides by 2
y=6
sub back
5x+8y=77
5x+8(6)=77
5x+48=77
minus 48 both sides
5x=29
divide both sides by 5
x=29/5
x=29/5
y=6
(x,y)
(29/5,6) is the solution