Question

Consider a system of two linear equations in two variables. If the graphs of the equations are not the same line, is it possible for the system to have infinitely many solutions. Explain.

Answer 1

No

Explanation:

Solutions to systems of equations are points at which the lines of the equations intersect. Knowing this, only equations representing the same line would have infinitely many solutions because they would intersect at every one of each other's points - they're the exact same line. Therefore, if they are not the same line, they would not intersect at each and every point, and would not have infinitely many solutions.