Answer
Consistent
Solutions set: $\left\{\left(2,-3\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
\frac{1}{2}x+y=-2\\
x-2y=8
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}
\frac{1}{2}&1&|&-2\\1&-2&|&8\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_1=2r_1$
$\begin{bmatrix}
1&2&|&-4\\1&-2&|&8\end{bmatrix}$
$R_2=-r_1+r_2$
$\begin{bmatrix}1&2&|&-4\\0&-4&|&12\end{bmatrix}$
$R_2=-\dfrac{1}{4}r_2$
$\begin{bmatrix}1&2&|&-4\\0&1&|&-3\end{bmatrix}$
$R_1=-2r_2+r_1$
$\begin{bmatrix}1&0&|&2\\0&1&|&-3\end{bmatrix}$
Write the corresponding system of equations:
$\begin{cases}
1x+0y=2\\
0x+1y=-3
\end{cases}$
$\begin{cases}
x=2\\
y=-3
\end{cases}$
The system is consistent. The solution set is:
$\left\{\left(2,-3\right)\right\}$
