Answer
Consistent
Solution set: $\{(6,2)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+y=8\\
x-y=4
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}1&1&|&8\\1&-1&|&4\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_2=-r_1+r_2$
$\begin{bmatrix}1&1&|&8\\0&-2&|&-4\end{bmatrix}$
$R_2=-\dfrac{1}{2}r_2$
$\begin{bmatrix}1&1&|&8\\0&1&|&2\end{bmatrix}$
$R_1=-r_2+r_1$
$\begin{bmatrix}1&0&|&6\\0&1&|&2\end{bmatrix}$
Write the corresponding system of equations:
$\begin{cases}
x=6\\
y=2
\end{cases}$
The system is consistent. Its set solution is:
$\{(6,2)\}$
