Answer
The answer is
$ x=4 $ and $ 2 $.
Work Step by Step
The given equations are
$ x+y=6 $
$ x-y=2 $
The augmented matrix is
$\left[\begin{array}{cc|c}
1& 1 &6 \\
1&-1 &2 \\
\end{array}\right]$
Use matrix row operations to simplify.
Perform $ R_2\rightarrow R_2-1\cdot R_1 $
Multiply row one by $-1 $ and subtract from row 2 as shown below.
$\left[\begin{array}{cc|c}
1& 1 &6 \\
1-1 \cdot 1&-1-1 \cdot 1 &2-1 \cdot 6 \\
\end{array}\right]$
Simplify.
$\left[\begin{array}{cc|c}
1& 1 &6 \\
1-1 &-1-1 &2- 6 \\
\end{array}\right]$
$\left[\begin{array}{cc|c}
1& 1 &6 \\
0 &-2 &-4 \\
\end{array}\right]$
$ R_2\rightarrow \frac{R_2}{-2} $
Multiply row two by $ \frac{1}{-2} $
$\left[\begin{array}{cc|c}
1& 1 &6 \\
0 \cdot \frac{1}{-2}&-2\cdot \frac{1}{-2} &-4\cdot \frac{1}{-2} \\
\end{array}\right]$
Simplify.
$\left[\begin{array}{cc|c}
1& 1 &6 \\
0 &1 &2 \\
\end{array}\right]$
Use back substitution to find the system's solution.
$ x+y=6 $
$ y=2$ Substitute into above equation.
$ x+2=6 $
$ x=4 $.
