## Precalculus (6th Edition) Blitzer

We know that in a linear system of equations, each system has only one real solution. Let us take an example: \begin{align} & {{a}_{1}}x+{{b}_{1}}y={{c}_{1}} \\ & {{a}_{2}}x+{{b}_{2}}y={{c}_{2}} \\ \end{align} Are two linear equations, representing two lines. If ${{a}_{1}}\ne {{a}_{2}}$ and ${{b}_{1}}\ne {{b}_{2}}$ then these two lines intersect and the point of intersection in a solution. And if ${{a}_{1}}\ne {{a}_{2}}$ and ${{b}_{1}}\ne {{b}_{2}}$ then the two lines are parallel to each other and intersect nowhere. So, a linear system cannot have infinite solutions. Thus, the provided statement does not make sense.