Question

Use the table to answer the question.

This table compares the two systems. System B is incomplete, missing its second equation.
System A System B
7x+4y=−4

5x+8y=28

7x+4y=−4

?

Which of the following terms will make the systems equivalent?


(1 point)
Responses

12x+12y=24
12 x plus 12 y equals 24

−12x−12y=24
negative 12 x minus 12 y equals 24

−14x−8y=−8
negative 14 x minus 8 equals negative 8

−14x−8y=8

Answer 1

12x + 12y = 24

Reason: System A solves to (x,y) = (−4,6). Plugging into the choices, only 12x+12y=24 and −14x−8y=8 are satisfied by (−4,6). But −14x−8y=8 is just −2 times the first equation, so it would make the two equations dependent (infinitely many solutions). 12x+12y=24 is the sum of the two original equations and gives the same unique solution, so it makes the systems equivalent.