Laws That Deal with Electrical Currents Are Known as Kirchhoff $R _ { 1 } = 4$

Multiple Choice

Laws that deal with electrical currents are known as Kirchhoff s Laws. When Kirchhoff s Laws are applied to the electrical network shown in the figure, where $R _ { 1 } = 4$ ohms, $R _ { 2 } = 2$ ohms, $R _ { 3 } = 4$ ohms, $V _ { 1 } = 26$ volts, $V _ { 2 } = 14$ volts, the currents $I _ { 1 } , I _ { 2 }$ and $I _ { 3 }$ (in amps) are the solution of the system $$\left\{ \begin{array} { l } I _ { 1 } + I _ { 2 } - I _ { 3 } = 0 \\4 I _ { 1 } + 2 I _ { 3 } = 26 \\4 I _ { 1 } - 4 I _ { 2 } = 12\end{array} \right.$$ Find the current $I _ { 3 }$ .

A) $6$ amps
B) 5 amps
C) $8$ amps
D) $7$ amps
E) $4$ amps