2 Answers

JWC · Answer 1 · 2020-01-07T20:34:06+0000

Answer:

$\boxed{x=1, \y=-1, \ z=2}$

We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:

Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}$

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}$

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~( 1 )/( 5 )~ z&~=~( 2 )/( 5 )\end{array}$

Step 4: solve for z, then for y, then for x:

$( 1 )/( 5 ) ~ z & = ( 2 )/( 5 ) \\ \\ \boxed{z & = 2}$

$-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}$

By substituting
$y=-1 \ and \ z=2$ into the first equation, we get the
. So:

$x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}$