Trouble finding the current through this resistor in the circuit

[guyvsdcsniper]

Homework Statement

FIind the current through and the potential difference across the 100 ohm resistor.

Relevant Equations

junction rule. loop rule

I was following this problem up until they say we can they state I3= I1-I2. I understand why we can say that but I don't see how I can use that to get the system of equation in terms of I1 and I2 at the bottom. Could someone show me how this was done?

 

[TSny]

You have the two equations

Take the first of these two equations and substitute $I_3 = I_1-I_2$. This means to replace $I_3$ in the equation by the quantity $(I_1-I_2)$. Then simplify.

Do the same for the second equation.

Show your work so we can help with any particular step for which you have trouble.