How many real solutions are there that satisfy the two equations and ?

Source: NCTM Mathematics Teacher, September 2006

**Solution**

The graph of is a circle centered at the origin and radius = . The graph of is a hyperbola with vertices at and . The two graphs intersect at four points. There are four real solutions that satisfy the two equations.

**Answer**:

**Alternate solution**

Add the two equations

————————

Substitute the value of into the first equation

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