Answer
Consistent
Solution set: $\{(1,2)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+2y=5\\
x+y=3
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}1&2&|&5\\1&1&|&3\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_2=-r_1+r_2$
$\begin{bmatrix}1&2&|&5\\0&-1&|&-2\end{bmatrix}$
$R_2=-r_2$
$\begin{bmatrix}1&2&|&5\\0&1&|&2\end{bmatrix}$
$R_1=-2r_2+r_1$
$\begin{bmatrix}1&0&|&1\\0&1&|&2\end{bmatrix}$
Write the corresponding system of equations:
$\begin{cases}
x=1\\
y=2
\end{cases}$
The system is consistent. Its set solution is:
$\{(1,2)\}$
