Kirchoff's Rules Homework: Solving 3 Unknowns in a Circuit

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The discussion revolves around solving a circuit problem using Kirchhoff's Rules, focusing on three unknowns represented by currents I1, I2, and I3. The user has formulated three equations based on voltage sums but is confused about the presence of a third unknown in each equation. There's a suggestion that one of the equations may contain a typo regarding the coefficient of I3. Additionally, it is noted that one of the loops in the circuit does not include the battery, implying its voltage sum should equal zero. The user seeks assistance in organizing these equations into a 3X3 matrix for solution in Excel.
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Homework Statement


This is the circuit I'm working on:
cir.gif


Homework Equations


My equations are:
4.64v=-200I1-800I3
4.64v=750I3+800I2
4.64v=-200I1-750I3

The Attempt at a Solution


I should have a third unknown in each equation. I not seeing where I'm going wrong. I'm supposed to put this in a 3X3 matrix and have Excel solve for the simultaneous equations. Any help?
 
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There are three different loops that you can sum the voltages around in the problem. The one involving R2 and R3 does not include the battery. So the sum around that loop should be zero. Your first equation also has an 800I3. Typo?
 

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