Question

(( PLEASE HELP! ))

Two systems of equations are shown below:
System A:
2x + y = 5
-4x + 6y = -2
System B:
-10x + 19y = -1
-4x + 6y = -2

Which of the following statements is correct about the two systems of equations?

A: 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.

B: 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.

C: 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.

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 -12 to the first equation of system A and the second equations are identical.

Answer 1

B: 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:

Each of the first two answer choices suggests that the first equation of system A was added to something to get the first equation of system B. We can subtract the first equation of system A from that of system B to see what was added exactly:

(-10x +19y) -(2x +y) = (-1) -(5)

-12x +18y = -6

The coefficients of this equation are 3 times those of the second equation of either system, so choice B is an appropriate description.