Which system of equations has the same solution as the system below?

4x+5y=13 and 10x-8y = - 32

A:4x+5y=13 and 5x-4y = - 32

B:40x+50y=130 and 5x-4y=16

Neither.

But possibly B.

Step-by-step explanation:

A system of equations has the same solution if it can be reduced to the same equation by simplification.

For example, x+y=2 and y=1 has the solution x=1

likewise, 10x+10y=20 and 4y=4 has the solution x=1.

This is easy to see by dividing the first by 10 and the second equation by 4, leaving you with the original system x+y=2 and y=1.

For your case, none of the options are correct, but assuming you missed the negative sign on the 16 in system B, then it would be correct.

B. 40x+50y=130 and 5x-4y=-16

divide by 10 (equation 1) and multiply by 2 (equation 2):

B is now: 4x+5y=13 and 10x-8y=-32

Since B is exactly equivalent to the original system, their solutions must be the same.