Answer
$\left\{\left(\dfrac{28-y}{4},y\right)|y\text{ is any real number}\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+\dfrac{1}{4}y=7\\
8x+2y=56
\end{cases}$
The augmented matrix associated with the system is:
$A=\begin{bmatrix}1&\dfrac{1}{4}&|&7\\8&2&|&56\end{bmatrix}$
Multiply $R_1$ by -8 and add it to $R_2$:
$\begin{bmatrix}1&\dfrac{1}{4}&|&7\\0&0&|&0\end{bmatrix}$
As the last line contains only zeros, the system has infinitely many solutions.
$x+\dfrac{1}{4}y=7$
$x=7-\dfrac{1}{4}y$
$x=\dfrac{28-y}{4}$
The solution set is:
$\left\{\left(\dfrac{28-y}{4},y\right)|y\text{ is any real number}\right\}$
