Question

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

Answer 1

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)

Answer 2

$4x-y=2 \\ 2x+9y=-12 \\ \\ ---- \\ \\ 4x - y = 2 \\ \\ 4x - y + 4 = 2 + y \\ \\ 4x = 2 + y \\ \\ \frac{4x}{4} = \frac{2+y}{4} \\ \\ x = \frac{2+y}{4} \\ \\ 2 \frac{2+y}{4} + 9y = -12 \\ \\ 9y + \frac{y+2}{2} = -12 \\ \\ 2 \times 9y + 2 \frac{y+2}{2} = -2 \times 12 \\ \\ 19y + 2 = -24 \\ \\ 19y + 2 - 2 = -24 - 2 \\ \\ 19y = -26 \\ \\ \frac{19y}{19} = \frac{-26}{19} \\ \\ y = - \frac{26}{19}$

-----

$\\ \\ x = \frac{2+y}{4} \\ \\ y = - \frac{26}{19} \\ \\ x = \frac{2- \frac{26}{19} }{4} \\ \\ x = \frac{3}{19}$

-----

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