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Let $c$ be a real number, and consider the system of quadratic equations
y = x^2 - 9x + c,
y = 8x^2 - 13x.
For which values of $c$ does this system have:

(a) Exactly one real solution $(x,y)?$

(b) More than one real solution?

(c) No real solutions?

Solutions to the quadratics are $(x,y)$ pairs.

 Nov 15, 2023

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