How would you choose to reduce the system shown to a 2 × 2? Explain why you would choose this approach. –3x + y – 2z = 10 (1) 5x

Question

Ipatiy

1 month ago

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How would you choose to reduce the system shown to a 2 × 2? Explain why you would choose this approach. –3x + y – 2z = 10 (1) 5x

– 2y – 2z = 12 (2) x – y + z = 23 (3)

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-02-23T16:14:22+03:00

Answer:

To eliminate y, I will combine equations (1) and (3) due to the opposing coefficients. Subsequently, to eliminate y again, I will multiply equation (1) by 2 and add it to equation (2).

To remove z, I will subtract equation (2) from equation (1) since the coefficients are identical. For the next step of removing z, I will multiply equation (3) by 2 and add it to equation (1).

Step-by-step explanation:

Both equations in the 2 × 2 system must include the same variables.

All of this should be incorporated

Inessa [12.5K] · Answer 2 · 2026-02-23T16:12:24+03:00

-3x + y - 2z = 10 |* -1
3x - y +2z = -10
5x -2y -2z = 12
--------------------------- I combine these equations term by term
8x - 3y = 2

-3x + y - 2z =10 ⇒ -3x + y - 2z =10
x -y +z = 23 | *2 2x - 2y + 2z = 46
----------------------------- I combine equations
-x -y = 56

8x - 3y = 2
-x -y = 56

This represents the system after reduction (now with only two variables, x and y)