Question

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

Answer 1

option A

-2x + 4y = 4

-3x + 6y = 6

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.