Question

How do you solve the system of equations `6x - y + z = 21`, `4x + 2y - 3z = - 14`, and `x - 3y + 2z = 25`?

Answer 1

`x=10/3`, `y=-5` and `z=-4`

Explanation:

Combine the first and the third original equations (after enlarging the third by -6:

`6x=21+y-z`
`-6x=-150-18y+12z`
Now you will have
`0=-129-17y+11z` or
`17y-11z=-129` (1)

Next, enlarge the third original equation by -4 and combine with the second original equation (Yielding):
`4x=3z-2y-14`
`-4x=-100-12y+8z`
Combining these two: `0=-114-14y+11z`
or `14y-11z=-114` (2)

Now combine the derived equations ((1) and (2)) after multiplying the second by -1:
`17y-11z=-129`
`-14y+11z=114`
`3y=-15` and
`y=-5`

Put this value in (1) or (2)
`(17*-5)-11z=-129`
`11z=-129+85`
`z=-44/11`
`z=-4`

Now you can find x, using any original equation:
`6x-(-5)-4=21`
`6x+5-4=21`
`6x=21-1`
`x=20/6`
or `x=10/3`