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The Number of Solutions to a System


A system of linear-quadratic equations may have zero, one, or two real solutions.

The two graphs do not intersect. This system has no solution.

The two graphs intersect once. This system has one solution.

The two graphs intersect twice. This system has two solutions.


A system of quadratic-quadratic equations may have zero, one, two, or an infinite number of real solutions.

The two curves do not intersect. This system has no solution.

The two curves intersect once. This system has one solution.

The two curves intersect twice. This system has two solutions.

The two curves are coincident (one is on top of the other). This system has an infinite number of solutions.



 

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