Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: l solution are below. y y y 3 3 2 2 1 1 x −3 −2 −1 2 x −3 −2 −1 2 −1 −2 −3 x2 + y 2 ≥ 4 −1 −2 −1 −3 x2 − 2x + y 2 − 2y ≤ 0 Solution to the system. x 544 8.7.1 Systems of Equations and Matrices Exercises 1. Solve the following systems of nonlinear equations. Sketch the graph of both equations on the same set of axes to verify the solution set. (a) x2 − y = 4 x2 + y 2 = 4 (c) x2 + y 2 = 16 16x2 + 4y 2 = 64 (e) (b) x2 + y 2 = 4 x2 − y = 5 (d) x2 + y 2 = 16 9x2 − 16y 2 = 144 (f) x2 + y 2 = 16 =1 12 12 9 y − 16 x x2 + y 2 = 16 x−y = 2 2. Solve the following systems of nonlinear equations. Use a graph to help you avoid any potential extraneous solutions. (a) (b) (c) x2 − y 2 = x2 + 4 y 2 = √ x+1−y x2 + 4y 2 1 4 =0 =4 x + 2y 2 = 2 x2 + 4 y 2 = 4 (d) (x − 2)2 + y 2 = 1 x2 + 4 y 2 = 4 (e) x2 + y 2 = 25 y−x = 1 (f) x2 x2 + y 2 = 25 + (y − 3)2 = 10 y= x3 + 8 y = 10x − x2 (g) x2 + y 2 = 25 4x2 − 9y = 0 (h) 2 3y − 16x = 0 3. Carl and Mike start...
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