Question

Question #9ab83

Answer 1

`x=4,y=0,z=-3`

Explanation:

Given three equation and three unknown
`x+y-z=7` .......(1)
`-2x+2y-z=-5` .......(2)
`3x-3y+2z=6` ......(3)

Step 1. Eliminate one unknown from first two equations. Let us take `z`

Subtracting (2) from (1) we get
`(x+y-z)-(-2x+2y-z)=7-(-5)`
`=>x+y-z+2x-2y+z=7+5`
`=>3x-y=12` ......(4)

Step 2. Eliminate same unknown from next two equations. (one can choose last two as well).

Multiplying (2) with `2` and adding (3)
`2xx(-2x+2y-z)+(3x-3y+2z)=2xx(-5)+6`
`=>-4x+4y-2z+3x-3y+2z=-10+6`
`=>-x+y=-4` .....(5)

We now have two equations (4) and (5) with two unknowns.
Step 3. Eliminate one unknown from these two equations.

We see that if we add these two we eliminate `y`. We get
`3x-y+(-x+y)=12+(-4)`
`=>3x-y-x+y=12-4`
`=>2x=8`
`=>x=8/2`
`=>x=4`

Step 4. Insert this value of `x` in either (4) or (5) to obtain `y`. Let us choose (5)

`-4+y=-4`
`y=-4+4`
`y=0`

Step 5. Insert these values of `x and y` in any of (1), (2) or (3) to obtain `z`. Let us choose (1)

`4+0-z=7`
`=>z=4-7`
`=>z=-3`