Chapter 9, Problem 3CLT

To determine

Solve the system by the specified method.

Answer to Problem 3CLT

  $(5,-2,-2)$

Explanation of Solution

Calculation:

Let us try to solve the system by elimination method

The equations are,

  $\begin{array}{l}-2x+4y-z=-\mathrm{16.......}\left(1\right)\\ x-2y+2z=\mathrm{5..............}\left(2\right)\\ x-3y-z=\mathrm{13..............}\left(3\right)\end{array}$

Multiplying Equation $2$ by $2$ and adding to equation $1$ , we get

  $\begin{array}{l}-2x+4y-z=-16\\ \begin{array}{ccc}2x-& 4y+4z=10& \end{array}\\ \begin{array}{ccc}\begin{array}{l}3z=-6\\ z=-2\end{array}& & \end{array}\end{array}$

Multiplying Equation $\left(2\right)$ by $(-1)$ and adding to Equation $3$ , we get

  $\begin{array}{l}-x+2y-2z=-5\\ \begin{array}{c}x-3y-z=13\end{array}\\ -y-3z=8\end{array}$

Substituting the value of $z=-2$ in the equation above, we get

  $\begin{array}{l}-y-3(-2)=8\\ y=-2\end{array}$

Substituting the value of $y=-2,z=-2$ in Equation $\left(2\right)$ we get

  $\begin{array}{l}x-2(-2)+2(-2)=5\\ x=5\end{array}$

Hence, solving by elimination method, we get $(5,-2,-2)$ .