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