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

One solution

or no solution

or an infinite number of solutions

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.

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