1) Let's solve the system
2x -3y = 60
y= 5x +6 ⇒ -5x+y=6
2x -3y = 60
-5x+y=6 Multiply by 3
2x -3y = 60
-15x+3y=18
--------------------------
-13x = 78 Divide both sides by -13
x = -6
2) Let's plug that into one of those equations, usually the simplest one
-5(-6) +y = 6
30 +y =6
y= 6-30
y=-24
3) As we can see the solution for that system is S={-6,-24}
So the answer is (-6, -24)