College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.6 - Systems of Nonlinear Equations - 8.6 Assess Your Understanding - Page 614: 8

Answer

$(-2,0)$ and $(-1.2,1.6) $

Work Step by Step

$\left\{\begin{array}{l}{y=\sqrt{4-x^{2}}}\\{y=2x+4}\end{array}\right.$ Graphed with desmos.com/calculator. Substitute y into the second equation, $\begin{aligned}\sqrt{4-x^{2}}&=2x+4\\ 4-x^{2}&=4x^{2}+16x+16\\ 5x^{2}+16x+12&=0\end{aligned}$ ... use the quadratic formula $x=\displaystyle \frac{-16\pm\sqrt{256-4(5)(12)}}{2(5)}=\frac{-16\pm\sqrt{16}}{10}\\=-1.6\pm 0.4$ $\left[\begin{array}{ll} x=-2.0 & x=-1.2\\ \text{... back -substitute} & \\ & \\ y=2(-2)+4 & y=2(-1.2)+4\\ y=0 & y=-2.4+4\\ & y=1.6\\ (-2,0) & (-1.2,1.6)\\ & \end{array}\right]$
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