<s>[INST] Is it possible to find solution of this system of equations? Following is augmented matrix which has been reduced to row echelon form by using row operations. So when I convert it to system of equations I would get 3 equations with 5 unknowns. Is it possible to find values of 5 unknowns in 3 equations? Is it true that at most one can solve equations with 3 unknowns in 3 equations? 
$$
\left[
\begin{array}{rrrrr|r}
    1 & 7& -2 & 0 & -8 & -3 \\
    0 & 0 &  1 & 1 &  6 &  5 \\
    0 & 0 &  0 & 1 &  3 &  9 \\
    0 & 0 &  0 & 0 &  0 &  0 \\
\end{array}
\right]
$$
 [/INST] 
Is it possible to find values of 5 unknowns in 3 equations?

Yes, the solutions of your system form a 2 dimensional subspace of $F^5$, where $F$ is your field, e.g. $F = \mathbb{R}$.
$$
\left[
\begin{array}{rrrrr|r}
    1 & 7 & -2 & 0 & -8 & -3 \\
    0 & 0 &  1 & 1 &  6 &  5 \\
    0 & 0 &  0 & 1 &  3 &  9 \\
    0 & 0 &  0 & 0 &  0 &  0 \\
\end{array}
\right]
\to
\left[
\begin{array}{rrrrr|r}
    1 & 7 &  0 & 2 &  4 &  7 \\
    0 & 0 &  1 & 1 &  6 &  5 \\
    0 & 0 &  0 & 1 &  3 &  9 \\
    0 & 0 &  0 & 0 &  0 &  0 \\
\end{array}
\right]
\to
\left[
\begin{array}{rrrrr|r}
    1 & 7 &  0 & 0 & -2 &-11 \\
    0 & 0 &  1 & 0 &  3 & -4 \\
    0 & 0 &  0 & 1 &  3 &  9 \\
    0 & 0 &  0 & 0 &  0 &  0 \\
\end{array}
\right]
$$
E.g.
$$
x_5 = t \\
x_4 + 3t = 9 \iff x_4 = 9 - 3t \\
x_3 + 3t = -4 \iff x_3 = -4 - 3t \\
x_2 = s \\
x_1 + 7s - 2t = -11 \iff x_1 = -11 - 7s + 2t
$$
then
$$
x = \{ (-11-7s+2t, s, -4 - 3t, 9-3t, t) \mid s, t \in F \}
$$
</s>