Question

A system of linear equations in two variables can have _____ solutions

Answer 1

If the lines are parallel (have the same slope but different intercepts) . . .
     no solution, because they never cross.

If the lines have different slopes . . .
     one solution, because they have exactly one common point.   

If the lines have the same slope and the same intercept . . .
     infinitely many solutions, because every point on one line is also a point on
     the other line, one lays right on top of the other, and when you look at them on
     the graph, it looks like only one line.

Answer 2

One solution
or no solution
or an infinite number of solutions