Solve the System of Linear Equations$\left\{ \begin{array} { r }
x + z = 2 \
y + 2 z = 7 \
- x + z = 4
\end{array} \right.$

Question

Solve the System of Linear Equations$\left\{ \begin{array} { r } 
x + z = 2 \
y + 2 z = 7 \
- x + z = 4
\end{array} \right.$

Examlex · Accepted Answer

The Answer is

\left[ \begin{array} { c c c c } 1 & 0 & 1 & 2 \0 & 1 & 2 & 7 \- 1 & 0 & 1 & 4\end{array} ight]

\begin{array} { c } \Rightarrow \R _ {3 } + R _ { 1 } ightarrow R _ { 3 }\end{array}

\left[ \begin{array} { l l l l } 1 & 0 & 1 & 2 \0 & 1 & 2 & 7 \0 & 0 & 2 & 6\end{array} ight]

\begin{array} { c } R _ { 1 } - \frac { 1 } { 2 } R _ {3 } ightarrow R _ { 1 } \\Rightarrow \R _ { 2 } - R _ { 3 } ightarrow R _ { 2 }\end{array}

\left[ \begin{array} { c c c c } 1 & 0 & 0 & - 1 \0 & 1 & 0 & 1 \0 & 0 & 2 & 6\end{array} ight]

\begin{array} { c } \Rightarrow \\frac { 1 } { 2 } R _ { 3 }\end{array}

\left[ \begin{array} { c c c c } 1 & 0 & 0 & - 1 \0 & 1 & 0 & 1 \0 & 0 & 1 & 3\end{array} ight]

, so the solution is

x = - 1

,

y = 1

,

z = 3

.

Solve the System of Linear Equations $\left\{ \begin{array} { r } x + z = 2 \\y + 2 z = 7 \\- x + z = 4\end{array} \right.$