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

Answer:

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).

Step-by-step explanation:

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

All of this should be included