Final answer:
A system of linear equations cannot have exactly two solutions; it can only have a single unique solution, infinitely many solutions, or no solution at all.
Step-by-step explanation:
In the context of linear equations, it is not possible for a system to have two distinct solutions if it does not have infinitely many solutions. A system of linear equations can either have a single unique solution, infinitely many solutions, or no solution at all. This is determined by the relationships between the equations in the system. If the lines represented by the equations intersect at a single point, the system has one solution; if the lines coincide, there are infinitely many solutions; and if the lines are parallel and distinct, there is no solution.
An important distinction is that quadratic functions, which are second-order polynomials, can indeed have two solutions due to the presence of a squared term. However, this property is not applicable to linear equations, which are first-order polynomials and therefore do not have squared terms.