There are only three options! A system of linear equations can have...

• No solution (in this case the system is called inconsistent)

• One solution (in this case the solution is called unique)

• Infinitely many solutions (in this case the system is called dependent)

(If a system has either one solution or infinitely many solutions, it is called consistent.) 

Let's consider (for example) the case where we have two linear equations in two variables. In this case, we can think of each equation giving us a line in the coordinate plane. Solutions correspond to the intersection point(s) of the two lines. If we assume that the lines intersect at two points, this means that both lines go through both points, and so the two lines are sitting on top of each other. This means that there are infinitely many solutions. 

We use parameters to express the solution whenever the system has infinitely many solutions. It's not enough to simply say that there are infinitely many solutions; we need a way to describe these infinite solutions. We can't list them all out (because there are infinitely many), so we use a parameter to help us describe which points are solutions (and therefore which points are not solutions). 

• Graphically, you can think of the equilibrium point as the intersection of the supply and demand functions (if you were to graph both functions on the same set of axes). 

• In the context of the problem, the equilibrium point gives the number of units and the price that satisfy both the supply and demand functions. 

Check out the WebAssign Frequently Asked Questions page for the answer to this question.