Question

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)

Answer 1

-3x + y - 2z = 10 |* -1
3x - y +2z = -10
5x -2y -2z = 12
--------------------------- I add 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 add these eq.
-x -y = 56

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

this is the system after i reduce it ( it has only two variables x and y)

Answer 2

Eliminate y by adding equations (1) and (3) because the coefficients on y are opposites. Then eliminate y by multiplying equation (1) by 2 and adding it to equation (2).

Eliminate z by subtracting equations (1) and (2) because the coefficients are the same. Then eliminate z by multiplying equation (3) by 2 and adding it to equation (1).

Explanation:

The variables have to be the same in both equations in the 2 × 2 system.

All of this should be included