Question

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

Answer 1

Answer:

Please check the explanation below.

Step-by-step 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 $-z-4=-4$

$-z-4=-4$

$-z=0$

$\frac{-z}{-1}=\frac{0}{-1}$

$z=0$

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

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

$x=4-3y-0$

$x=-3y+4$

Therefore,

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

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