What is the solution of the system? use elimination.

-12x - y = 6

17x + y = 4

Add up the equations to get

-12x-y = 6
17x+y = 4

5x+0y = 10

which means 5x = 10
Divide both sides by 5 to get 

5x = 10
5x/5 = 10/5
x = 2

Now use x = 2 to find y
-12x - y = 6
-12(2) - y = 6
-24 - y = 6
-24 - y + 24 = 6+24
-y = 30
y = -30

If x = 2, then y = -30
The two values pair up to get the ordered pair (x,y) = (2,-30)

The solution of the system is (2,-30)

The two lines intersect at the point (2,-30)