Choose a system of equations with the same solution as the following system:

6x + 2y = - 6

3x - 4y = - 18

A) 8x + 4y = - 4

17x + 2y = - 28

B) 12x + 4y = 12

21x + 2y = - 36

C) 6x + 8y = - 36

15x + 6y = - 60

D) 6x + y = 15

15x - y = - 9

Option A.

Step-by-step explanation:

We are given 6x+2y = -6 ... (1) and 3x-4y=-18 ... (2)

Solving equations (1) and (2) we get

12x+3x = -30, ⇒x = - 2 and from equation (1), 2y = - 6-6 (-2) = 6, ⇒ y=3

Therefore, the solution for the given set of equations is x = - 2 and y=3

A) Solving the equations 8x+4y = - 4 ... (3) and 17x+2y = -28, we get

8x - 34x = - 4 - (-56) = 52, ⇒-26x = 52, ⇒x=-2 and from equation) (3), we get - 16+4y = -4, ⇒ y=3

Therefore, the solution x=-2 and y = 3 match with the original solution.

B) Solving the equations 12x + 4y = 12 ... (4) and 21x + 2y = - 36, we get

12x - 42x = 12 - (-72) = 84, ⇒-30x = 84, ⇒x=-84/30.

Therefore, the solution x=-84/30 does not match with the original solution.

C) Solving the equations 6x + 8y = - 36 ... (4) and 15x + 6y = - 60, we get 18x - 60x = - 108 - (-240) = 132, ⇒-42x = 132, ⇒x=-132/42

Therefore, the solution x=--3 do not match with the original solution.

D) Solving the equations 6x + y = 15 ... (5) and 15x - y = - 9, we get 6x + 15x = 6, ⇒21x = 6, ⇒x=2/7

Therefore, the solution x=2/7 do not match with the original solution.

Therefore, option A) will have the same solution. (Answer)