How Do You Solve Kirchhoff's Loop Equations for Currents I1, I2, and I3?

[StephenDoty]

My professor gave us the three equations for a circuit and said to find I1, I2, and I3 However, I cannot figure out how to solve it.

The equations:

I1 + I2 = I3

5 - 10*I1 -10 - 5*I3 = 0

5 - 5*I2 - 5*I3 - 10 = 0

Every time I try to solve it I end up with two unknown variables. How would you solve them? I am having difficulty solving systems of equations. A step by step guide would be a great help.
Thanks.
Stephen

 

[Hootenanny]

Try substituting the the first equation into the second and third equations to eliminate I3. You will then have two equations with two unknowns, which you can solve my eliminating a further variable.

Alternatively if you are comfortable with matrices you can form a matrix equation and put the coefficient matrix into REF.