Question

Given the system of linear equations. Choose all of the options that could be used to solve the system using addition
{x + y = 7
{2x + y = 5

Multiply the first equation by -1 and add the equations together.
Multiply the first equation by 2 and the second equation by -1, then add the equations together.
Multiply the first equation by -2 and add the equations together.
Multiply the second equation by -1 and add the equations together.
Multiply the second equation by -1 and the first equation by -1, then add the equations together.

Answer 1

All except the last one. Options A, B, C, and D work; E does not.

Quick checks:
- A: (-1)*(x+y=7) → -x-y=-7. Add with 2x+y=5 → x = -2.
- B: 2*(x+y=7) → 2x+2y=14; (-1)*(2x+y=5) → -2x-y=-5. Add → y = 9.
- C: (-2)*(x+y=7) → -2x-2y=-14. Add with 2x+y=5 → -y = -9 → y = 9.
- D: (-1)*(2x+y=5) → -2x-y=-5. Add with x+y=7 → -x = 2 → x = -2.

E: (-1)*(both equations) gives -x-y=-7 and -2x-y=-5; adding does not eliminate a variable (y or x), so it doesn't directly solve by elimination.