Question

his table presents two systems of linear equations, System A and System B, with System B having a missing second equation.
System A System B
5x+2y=−3

3x+3y=9

3x+3y=9

?

Which of the following terms will make the systems equivalent?

(1 point)
Responses

−10x+4y=6
negative 10 x plus 4 y equals 6

−8x−5y=6
negative 8 x minus 5 y equals 6

−10x−4y=−6
negative 10 x minus 4 y equals negative 6

8x+5y=6

Answer 1

Solve System A:
5x+2y=−3 and 3x+3y=9 → multiply first by 3 and second by −2: 15x+6y=−9, −6x−6y=−18; add → 9x=−27 → x=−3. Then 3(−3)+3y=9 → y=6. So the solution is (−3,6).

Check which choice is satisfied by (−3,6):
- 8x+5y = 8(−3)+5(6)=−24+30=6, so 8x+5y=6 holds.

Thus 8x+5y=6 makes System B equivalent.