Question

Select the correct answer.

Solve the system of equations below.

-3x + 6y = 9
5x + 7y + -49

A. (-7, -2)
B.(1, -2)
C.(-2, -7)
D.(-2, 1/2)

Answer 1

A) ( -7,-2)

Explanation:

-3x + 6y = 9 ⇒ multiply by 5⇒(5) -3x + (5)6y = (5)9 ⇒ -15x + 30y = 45

5x + 7y = -49 ⇒ multiply by 3⇒3(5x) + (3) 7y = (3) -49 ⇒15x + 21y = -147

Add the two bold equations together and solve for y

15x + 30y = 45

-15x + 21y = -147

51y = -102 Divide both sides by 51

`(51y)/(51)` =
`(-102)/(51)`

y = -2

Substitute -2 into either of the two original equation to solve for x.

-3x + 6y = 9

-3x + 6(-2) = 9

-3x - 12 = 9 Add 12 to both sides

-3x -12 + 12 = 9 + 12

-3X = 21 Divide both sides by -3

`(-3x)/(-3)` =
`(21)/(-3)`

x = -7

Solution: (-7, -2)

Check:

-3x + 6y = 9

-3(-7) + 6(-2) = 9

21 -12 = 9

9 = 9 checks

5x + 7y = -49

5(-7) + 7(-2) = -49

-35 -14 = -49

-49 = -49 Checks