We are ask to use the elimination method to solve the system:
- 3 x + 4 y = - 18
x + 2 y = - 4
So we opt to eliminate the term in "x" since they have opposite signs already in the equations. We need though to have a "3 x" in the second equation, so we are going to multiply the full second equation by 3:
3 ( x + 2 y) = 3 (- 4)
3 x + 6 y = - 12
now we are going to combine term by term this modified second equation and the first one as shown below:
- 3 x + 4 y = - 18
3 x + 6 y = - 12
_____________
0 + 4 y + 6 y = -18 - 12
10 y = - 30
divide both sides by 10 to isolate y completely
y = - 30 / 10
y = - 3
Now we use this answer in the original second equation to solve for x:
x + 2 y = -4
x + 2 (- 3) = -4
x - 6 = -4
add 6 to both sides to isolate x completely on the left
x = -4 + 6
x = 2
Then the answer to the system is x = 2 and y = -3 which makes the coordinate pair: (2, -3)