Question

Two systems of equations are shown:

System A:
6x + y = 2
−x − y = −3
System B:
2x − 3y = −10
−x − y = −3
Which of the following statements is correct about the two systems of equations?

(A) The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.

(B) They will have the same solution because the first equations of both the systems have the same graph.

(C) They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.

(D) The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.

Answer 1

Hello

Im pretty sure its C

Answer 2

option C.

Explanation:

we have

System A

`6x+y=2` ---> first equation system A

`-x-y=-3` ----> second equation system A

Multiply the second equation by 4 both sides

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

`-4x-4y=-12`

Adds this equation to the first equation system A

`-4x-4y=-12\\6x+y=2\\-----\\-4x+6x-4y+y=-12+2`

`2x-3y=-10` ----> first equation system B

`-x-y=-3` ----> second equation system B

so

The first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A

The second equations are identical

therefore

They will have the same solution