Question

6x+18y+6z=24, -x-3y-2z=-4, 2x+6y+2z=8

Answer 1

Please check the explanation below.

Explanation:

Given the equations

`6x+18y+6z=24,\:-x-3y-2z=-4,\:2x+6y+2z=8\:\:`

Steps to solve

`\begin{bmatrix}6x+18y+6z=24\\ -x-3y-2z=-4\\ 2x+6y+2z=8\end{bmatrix}`

`\mathrm{Subsititute\:}x=4-3y-z`

`\begin{bmatrix}-\left(4-3y-z\right)-3y-2z=-4\\ 2\left(4-3y-z\right)+6y+2z=8\end{bmatrix}`

As

`-\left(4-3y-z\right)-3y-2z=-4`

`-z-4=-4`

and

`2\left(4-3y-z\right)+6y+2z=8`

`8=8`

so

`\begin{bmatrix}-z-4=-4\\ 8=8\end{bmatrix}`

Isolating z for
`-z-4=-4`

`-z-4=-4`

`-z=0`

`(-z)/(-1)=(0)/(-1)`

`z=0`

`\mathrm{For\:}x=4-3y-z`

`\mathrm{Expressing\:}x\mathrm{\:in\:terms\:of\:}y`

`x=4-3y-0`

`x=-3y+4`

Therefore,

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=-3y+4,\:z=0`