934 CHAPTER 9 Systems and Matrices 4. Refer to the system in Exercise 2. The other solution with real components has x-value -2. What is the y-value of this solution? 5. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)? x2 + y = 2 (1) x - y = 0 (2) 6. If we want to solve the following nonlinear system by eliminating the y2 terms, by what number should we multiply equation (2)? x2 + 3y2 = 4 (1) x2 - y2 = 0 (2) Concept Check Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations. 7. x2 = y - 1 y = 3x + 5 x 1 0 5 10 15 –1 2 3 4 x2 = y – 1 y = 3x + 5 y (–1, 2) (4, 17) 8. 2x2 = 3y + 23 y = 2x - 5 x 0 2x2 = 3y + 23 y = 2x – 5 y (4, 3) (–1, –7) 9. x2 + y2 = 5 -3x + 4y = 2 x x2 + y2 = 5 –3x + 4y = 2 (–2, –1) y ( ) , 38 25 41 25 10. x + y = -3 x2 + y2 = 45 x (–6, 3) (3, –6) x + y = –3 x2 + y2 = 45 3 3 y 11. y = 3x2 x2 + y2 = 10 x (–1, 3) (1, 3) y = 3x2 x2 + y2 = 10 3 0 1 y 12. y = - 4 9 x2 x2 + y2 = 25 x (–3, –4) (3, –4) 5 –4 0 3 5 y y = – x2 x2 + y2 = 25 4 9 Concept Check Answer each question. 13. In Example 1, we solved the following system. How can we tell, before doing any work, that this system cannot have more than two solutions? x2 - y = 4 x + y = -2
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