Use the linear combination method to solve the system of equations. explain each step of the solution.

-3x+7y=-16.

-9x+5y=16.

solution is (x, y) → ( - 4, - 4)

- 3x + 7y = - 16 → (1)

- 9x + 5y = 16 → (2)

multiply all terms in (1) by - 3. This will make the x-terms cancel out in the next step

9x - 21y = 48 → (3)

add (2) and (3) term by term to eliminate x

( - 9x + 9x) + (5y - 21y) = (16 + 48)

- 16y = 64 (divide both sides by - 16)

y = - 4

substitute y = - 4 into (1) or (2) and solve for x

(2) → - 9x - 20 = 16 (add 20 to both sides)

- 9x = 36 (divide both sides by - 9)

x = - 4

solution is (x, y) → ( - 4, - 4)