Solve the system of equations by multiplying and adding. Enter the solution as an ordered pair. \left \{ {{5x+2y=-7} \atop {4x-y=-16}} \right.

Question

Solve the system of equations by multiplying and adding. Enter the solution as an ordered pair.


`\left \{ {{5x+2y=-7} \atop {4x-y=-16}} \right.`

Answer 1

(x, y) = (- 3, 4)

Explanation:

Given the 2 equations

5x + 2y = - 7 → (1)

4x - y = - 16 → (2)

multiply all terms in (2) by 2

8x - 2y = - 32 → (3)

Add (1) and (3) term by term

(5x + 8x) + (2y - 2y) = (- 7 - 32)

13x = - 39 ( divide both sides by 13 )

x = - 3

Substitute x = - 3 into either (1) or (2) and solve for y

substituting in (1) gives

(5 × - 3) + 2y = - 7

- 15 + 2y = - 7 ( add 15 to both sides )

2y = 8 ( divide both sides by 2 )

y = 4

solution is (- 3, 4 )