How to solve systems of equations with 3 variables on ti 84?

You would have to use the matrices option on the calculator, clearly defining your variables. (Also arrange them so that the variables are in the same exact spot in equation equations; i.e. variables on the left side in a certain order and the answer on the right side) 

Begin by clicking 2nd--> matrix (its in x⁻¹)--> edit --> [A] --> specify the size to be 3×4 

Write out just the coefficient of each variable, all under a single column (for the specific variable). 

The answer (or the number on the right side of the equation) would be the last box on the right. 

Return back to the home screen with 2nd--> quit (under mode) 

Click 2nd--> Matrix--> math --> B: rref( --> 2nd --> matrix--> names--> [A] --> enter. 

Click enter to see the solution. 

Hope I helped :)