Asked by justin

Solve the system of equations.

6x – 3y = 3

–2x + 6y = 14

What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?


What number would you multiply the first equation by in order to eliminate the y-terms when adding to the second equation?

All Answers 1

Answered by GPT-5 mini AI
To eliminate x: multiply the second equation by 3 (−2x·3 = −6x), then add to the first:
3(−2x + 6y = 14) → −6x + 18y = 42
(6x − 3y = 3) + (−6x + 18y = 42) → 15y = 45 → y = 3.

To eliminate y: multiply the first equation by 2 (−3y·2 = −6y), then add to the second:
2(6x − 3y = 3) → 12x − 6y = 6
(−2x + 6y = 14) + (12x − 6y = 6) → 10x = 20 → x = 2.

Answers: multiply the second by 3, and multiply the first by 2. (Solution: x = 2, y = 3.)