Solving a system of equations with less equations than variables For my discrete math/linear algebra class, one of our homework problems reads as follows:
Use backsubstitution to solve the following system of equations and obtain the general     
solution.
3x + 4y + 7z - 3t = 3 
0x + 5y + 3z = 40

Now, I've always been taught that you need as many equations as variables to solve a system of equations. Is there a way to do this where you don't need as many equations as variables? Or would I be correct in making x and t both equal 1 so that they cancel out and then solve the system that way?

Are you familiar with Gaussian elimination for non-square linear systems? You want to construct the augmented matrix
$$ \begin{bmatrix} 3 & 4 & 7 & -3 & | & 3 \\ 0 & 5 & 3 & 0 & | & 40 \end{bmatrix}$$
and perform back-substitution to obtain a reduced row-echelon form. You do not want to arbitrarily set $x = t = 1$, because then you are not obtaining every solution. 
