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: 9

Answer

$(1,1)$

Work Step by Step

$\left\{\begin{array}{l}{y=\sqrt{x}}\\{y=2-x}\end{array}\right.$ Graphed with desmos.com/calculator. Restrictions: $x\geq 0,y\geq 0$ Substitute y into the second equation, square both sides $\begin{aligned}\sqrt{x}&=2-x\\x&=4-4x+x^{2}\\0&=x^{2}-5x+4\\(x-4)(x-1)&=0\end{aligned}$ $\left[\begin{array}{ll} x=1 & x=4\\ \text{... back -substitute} & \\ & \\ y=2-1 & y=2-4\\ y=1 & y=-2\\ & \text{discard,}\\ (1,1) & \text{negative} \\ & \end{array}\right]$
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