IXL | Find the number of solutions to a system of equations

How many solutions does the system of equations below have?

no solution

one solution

infinitely many solutions

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Learn with an example

How many solutions does the system of equations below have?

no solution

one solution

infinitely many solutions

A system of two equations can be classified as follows:

If the slopes are the same but the y-intercepts are different, the system has no solution.

If the slopes are different, the system has one solution.

If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

The slopes are the same but the y-intercepts are different, so the lines are parallel and never intersect. The system has no solution.

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