For the circuit shown in the figure below, we wish to find the currents I_{1}, I_{2}, and I_{3}.

(a) Use Kirchhoff's rules to complete the equation for the upper loop. (Use any variable or symbol stated above as necessary. All currents are given in amperes. Do not enter any units.)

(b) Use Kirchhoff's rules to complete the equation for the lower loop. (Use any variable or symbol stated above as necessary. All currents are given in amperes. Do not enter any units.)

(c) Use Kirchhoff's rules to obtain an equation for the junction on the left side. (Use any variable or symbol stated above as necessary. All currents are given in amperes.)

(d) Solve the junction equation for I_{3}.

(e) Using the equation found in part (d), eliminate I_{3} from the equation found in part (b). (Use any variable or symbol stated above as necessary. All currents are given in amperes. Do not enter any units.)

(f) Solve the equations found in part (a) and part (e) simultaneously for the two unknowns for I_{1} and I_{2}, respectively.

(g) Substitute the answers found in part (f) into the junction equation found in part (d), solving for I_{3}.

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