Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 13 - Section 13.4 - Nonlinear Inequalities and Systems of Inequalities - Exercise Set - Page 954: 29

Answer

Please see the graph.

Work Step by Step

Blue line: $\frac{x^{2}}{4}+\ \frac{y^{2}}{9}\ge1$ Green line: $x^2+y^2\ge4$ $\frac{x^{2}}{4}+\ \frac{y^{2}}{9}\ge1$ This is the equation of an ellipse. $x^2+y^2\ge4$ This inequality is similar to the equation $x^2+y^2 =4$, which is the equation of a circle with radius 2. For both inequalities, if a point is outside the shape, then it is part of the solution set. The ellipse has a larger major axis, so the solution set for the ellipse includes all solutions for the circle.
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