Answer
$I_1=\frac{19}{28}$.
$I_2=\frac{2}{7}$
$I_3=\frac{131}{196}$
Work Step by Step
$\begin{cases}
I_1+I_2-I_3=0\\
16I_1-8I_2=4\\
8I_2+4I_3=5
\end{cases}$
Adding Equation 2 and Equation 3, results in new Equation 2.
$\begin{cases}
16I_1-8I_2=4\\
4I_3+8I_2=5\\
-- -- -- -- -\\
16I_1+4I_3=9
\end{cases}$
Multiplying Equation 1 by -8 and adding it to equation 3, results in new equation 3.
$\begin{cases}
-8I_1-8I_2+8I_3=0\\
8I_2+4I_3=5\\
-- -- -- -- --\\
-8I_1+12I_3=5
\end{cases}$
Multiplying the new equation 3 by 2 and adding it to the new equation 2.
$\begin{cases}
16I_1+4I_3=9\\
-16I_1+24I_3=10\\
-- -- -- -- --\\
28I_3=19
\end{cases}$
Thus, $I_1=\frac{19}{28}$. Substituting back in, $I_2=\frac{2}{7}$ and $I_3=\frac{131}{196}$
