Give a solution to the following system of equations in parametric form: \begin{cases} 5x_1 + 3x_2 + 7x_3 -x_4 =8 \\ -2x_1 -x_2-3x_3+x_4=-2 \\ 2x_1+2x_2+2x_3+2x_4=8 \end{cases}
Could anyone help me figure out a solution to this question? Thanks a lot.
I tried to transform the augmented matrix to REF, and get those xs' relations with each other. However, it seemed that there are several free variables which prevent me from figuring out a true numerical solution to this system of linear equations.

This system can be written as the matrix equation
$$\begin{bmatrix}5&3&7&-1\\-2&-1&-3&1\\2&2&2&2\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix}=\begin{bmatrix}8\\-2\\8\end{bmatrix}$$
Row reduce the augmented matrix
$$\begin{bmatrix}5&3&7&-1&|&8\\-2&-1&-3&1&|&-2\\2&2&2&2&|&8\end{bmatrix}$$
to obtain the solution system.
