Simultaneous Equations From Kirchhoff's Rules

[00Formula00]

Homework Statement

For a Lab report I have to solve for three unknown currents from Kirchoff's Rules equations using simultaneous equation algebra, and I'm completely stumped.

Homework Equations

From Loop and junction equations, the three equations that I have are

I₁ + I₂ = I₃

I₁= (-I₃R₃ - V₂)/ (R₂)

I₂= (-I₃R₃+V₁)/(R₁)

The Attempt at a Solution

This is the farthest I have gotten, solving for I₃. Once I have expression for this I will be able to plug back into the I₁ and I₂ equations fairly easy.

(-I₃R₃R₂+ -I₃R₃R₁+ -V₂R₁) / (R₁R₂)

= I₃R₁R₂

Sorry If this is confusing. Thanks for any help in advance.

 

[llello]

You should just have to move all the terms with I3 to one side of the equation and factor out the current. That should give you an answer for I3.