Question

How do you solve 4x + 5y - 2z = 23, -6x + 2y + 7z = -14, and 8x + 3y + 3z = 11?

Answer 1

`x=1, y=3, z=-2`

Explanation:

`4x+5y-2z=23=>` eq-1
`-6x+2y+7z=-14=>` eq-2
`8x+3y+3z=11=>` eq-3

Eliminate `Z` between 1 & 2: multiply by 7 & 2 respectively, then add the equations:

`28x+35y-14z=161`
`-12x+4y+14z=-28`
`16x+39y=133=>` eq-4

Eliminate `Z` between 2 & 3: multiply by 3 & -7 respectively, then add the equations:

`-18x+6y+21z=-42`
`-56x-21y-21z=-77`
`-74x-15y=-119=>` eq-5

Eliminate `y` between 4 & 5: multiply by 15 & 39 respectively, then add the equations, `y's` cancel, solve for `x`:

`240x+585y=1995`
`-2886x-585y=-4641`
`-2646x=-2646`
`x=1=>` plug in eq-4 solve for `y`:
`39y=117`
`y=3=>` plug in for x & y in eq-1 solve for `z`:
`4+15-2z=23`
`-2z=4`
`z=-2`