Question

I need help solving. The answer is (2,-6)
Which ordered pair is the solution to the system of equations?

{x=1/2y+5
2x+3y=−14




(8, 9)

(−1, −12)

(18, 14)

(2, −6)

Answer 1

Since we are given x in terms of y, the most efficient way to solve it would be to substitute in the $\frac{1}{2}y+5$ for x in the second equation. So, we then have:

$2(\frac{y}{2}+5)+3y=-14 \implies \\ y+10+3y=-14 \implies \\ 4y+10=-14 \implies\\ 4y=-24 \implies \\ y=-6$

So, now that we have our y, we can find x. We can actually use either equation, top or bottom, to find x, but to be efficient we should use the top one since we have x in terms of y, so:

$x=\frac{-6}{2}+5 \implies \\ x=-3+5 \implies \\ x=2$

So, our ordered pair is (2,-6).