4x-y=2 2x+9y=-12 unsure how to solve

Simple, use the process of elimination to figure this out:

4x-y=2
2x+9y=-12

Convert these, to be able to find either x or y.

2(4x-y=2)   8x-2y=4   multiply by 2.
then
4(2x+9y=-12)  8x+36y=-48

Which makes them

8x-2y=4
-
8x+36y=-48

-38y=52

This simplified makes it y= -26/19.

Then plug y back into the original equation

4x-y=2

4x-(-26/19)=2

Making it x= 3/19.

Thus your Point of Intersection is at (3/19, -26/19)

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The final result is: x = 3/19 and y = -26/19.