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