How to solve for variables using a Matrix on TI-84?

Hit "2nd" and then "Matrix" on your calculator (above the X^-1 key). Then scroll over to "Edit", and edit any matrix by setting it to a 3 x 4 in this case and then imputing the coefficients. Next, exit out to the main screen, return to the matrix menu, scroll over to "Math" this time, and select "rref". Make sure you don't select "ref", it's "rref" - reduced row-echelon form. Return to the matrix menu one last time and select the one you've just edited. Voila, that should give you the answers.