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)

4th option is correct xy=-10

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