Answer
Consistent
Solution set: $\left\{\left(\dfrac{4}{3},\dfrac{1}{5}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x-5y=3\\
15x+5y=21
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}
3&-5&|&3\\15&5&|&21\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_2=-5r_1+r_2$
$\begin{bmatrix}
3&-5&|&3\\0&30&|&6\end{bmatrix}$
$R_1=\dfrac{1}{3}r_1$
$\begin{bmatrix}1&-\frac{5}{3}&|&1\\0&30&|&6\end{bmatrix}$
$R_2=\dfrac{1}{30}r_2$
$\begin{bmatrix}1&-\frac{5}{3}&|&1\\0&1&|&\frac{1}{5}\end{bmatrix}$
$R_1=\dfrac{5}{3}r_2+r_1$
$\begin{bmatrix}1&0&|&\frac{4}{3}\\0&1&|&\frac{1}{5}\end{bmatrix}$
Write the corresponding system of equations:
$\begin{cases}
1x+0y=\frac{4}{3}\\
0x+1y=\frac{1}{5}
\end{cases}$
$\begin{cases}
x=\frac{4}{3}\\
y=\frac{1}{5}
\end{cases}$
The system is consistent. The solution set is:
$\left\{\left(\dfrac{4}{3},\dfrac{1}{5}\right)\right\}$
