A student took a system of equations, multiplied the first equation by and the second equation by, then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?

A. - 2x+4y=4

-3x+6y=6

B. 3x+y=12

-3x+6y=6

C. 3x+6y=9

-2x-4y=4

D. 2x-4y=6

-3x+6y=9

option A

-2x + 4y = 4

-3x + 6y = 6

Step-by-step explanation:

In option A, if the student multiply the first equation by 3 and the second equation by - 2, then the equations become

-6x+12y = 12 and

6x-12y = -12

If she adds both equations, she will get 0 = 0

This means that the system has infinite number of solutions.

Hence, the student could have started with equations - 2x + 4y = 4 and - 3x + 6y = 6.