Circuit Analysis In Exercises 69 and 70 , consider the circuit in the figure. The currents $I_{1}, I_{2},$ and $I_{3},$ in amperes, are given by the solution of the system of linear equations
$$left{egin{aligned} 2 I_{1} &+4 I_{3}=E_{1} \ I_{2}+4 I_{3} &=E_{2} \ I_{1}+I_{2}-I_{3} &=0 end{aligned}
ight.$$
where $E_{1}$ and $E_{2}$ are voltages. Use the inverse of the coefficient matrix of this system to find the unknown currents for the voltages.
$$
E_{1}=10 ext { volts }, E_{2}=10
$$