Question

Two systems of equations are shown below: System A System B 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 Which of the following statements is correct about the two systems of equations? They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A. The value of x for System B will be −5 times the value of x for System A because the coefficient of x in the first equation of System B is −5 times the coefficient of x in the first equation of System A. 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 −12 to the first equation of System A and the second equations are identical.

Answer 1

They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

Explanation:

Answer 2

They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

Explanation:

System A

2x + y = 5 --> (1)

−4x + 6y = −2 --> (2)

(1) + 3×(2)

-10x + 19y = -1

System B

−10x + 19y = −1 --> (1)

-4x + 6y = −2 --> (2)