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?

You have $5y+3z=40.$ Express that as $3z=40-5y \implies z=\frac{40}{3}-\frac{5}{3}y$, and then plug that value of $z$ into your first equation. That's what back substitution essentially is. 
Your solution won't be a finite set of points; to have that, you need an independent equation for each variable you have (i.e., no equation is a linear combination of other equations in that matrix). You'll get to that soon enough in your course. 
Rather, your equation will be an infinite set of points. We describe them by the final reduced row-echelon form matrix that Christopher Wong alluded to. 
