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Consider the system of quadratic equations \begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*}where $c$ is a real number. (a) For what value(s) of $c$ will the system have exactly one solution $(x,y)?$ (b) For what value(s) of $c$ will the system have more than one real solution? (c) For what value(s) of $c$ will the system have no real solutions? Solutions to the quadratics are $(x,y)$ pairs. Your answers will be in terms of $c,$ but make sure you address both $x$ and $y$ for each part. Remember that if you get stuck on a homework problem, you can always ask on the message board! Click on the pencil icon V in the upper-right corner of the problem, and this will open a box where you can ask your question, which will be posted on the message board. You can also click on the speech bubble icon t, which will bring up any discussions on that problem.

 Jul 31, 2020
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(a) c = 7

(b) c < 7

(c) c > 7

 Aug 14, 2020

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