Kirchoff's Law equation 3 unknowns Help

[JonB]

Please could somebody help me with this Kirchoff's law question with explanations/working out? I've been on it for hours and cannot see where I'm going wrong!

Q. An electrical circuit comprises three closed loops giving the following equations for the currents i1, i2 and i3.

i1 + 8i2 + 3i3 = -31
3i1 - 2i2 + i3 = -5
2i1 - 3i2 + 2i3 = 6

Solve for i1, i2 and i3

Any help appreciated!

 

[Ackbach]

We have
$$
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
3 &-2 &1 &-5 \\
2 &-3 &2 &6
\end{array} \right]_{\begin{array}{rr}-3R_1+R_2 \mapsto R_2 \\ -2R_1+R_3 \mapsto R_3\end{array}} \to
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
0 &-26 &-8 &88 \\
0 &-19 &-4 &68
\end{array} \right]_{-\frac{19}{26}R_2 + R_3 \mapsto R_3} \to
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
0 &-26 &-8 &88 \\
0 &0 &\frac{24}{13} &\frac{48}{13}
\end{array} \right].
$$
Can you finish?