Answer
Consistent
Solution set: $\left\{\left(\dfrac{1}{2},\dfrac{3}{4}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x-4y=-2\\
3x+2y=3
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}2&-4&|&-2\\3&2&|&3\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_1=\dfrac{1}{2}r_1$
$\begin{bmatrix}1&-2&|&-1\\3&2&|&3\end{bmatrix}$
$R_1=-3r_1+r_2$
$\begin{bmatrix}1&-2&|&-1\\0&8&|&6\end{bmatrix}$
$R_2=\dfrac{1}{8}r_2$
$\begin{bmatrix}1&-2&|&-1\\0&1&|&\frac{3}{4}\end{bmatrix}$
$R_1=2r_2+r_1$
$\begin{bmatrix}1&0&|&\frac{1}{2}\\0&1&|&\frac{3}{4}\end{bmatrix}$
Write the corresponding system of equations:
$\begin{cases}
x=\frac{1}{2}\\
y=\frac{3}{4}
\end{cases}$
The system is consistent. Its set solution is:
$\left\{\left(\dfrac{1}{2},\dfrac{3}{4}\right)\right\}$
