algebra 3.5 practice

Name_________________________________________________________ Date __________ 3.5 Practice A In Exercises 1–4, solve the system by graphing. Check your solution(s). 2. y = ( x + 2) − 3...

Name_________________________________________________________ Date __________ 3.5 Practice A In Exercises 1–4, solve the system by graphing. Check your solution(s). 2. y = ( x + 2) − 3 2 1. y = x + 6 y = 1 ( x + 6) y = −3 2 2 3. y = − x + 3 4. y = 2 x 2 − 8 x + 5 y = 3x 2 − 4 x + 3 y = 2x − 3 In Exercises 5 and 6, solve the system of nonlinear equations using the graph. 5. y 6. y 2 2 −4 −2 2 4 x −4 −2 2 4 x −6 In Exercises 7–10, solve the system by substitution. 7. y = x −4 8. x 2 + y 2 = 25 y = x2 − 4 x y = 5− x 9. x 2 + y 2 = 1 10. y = 7 x =1 3x − 6 = 4 x 2 − y In Exercises 11–14, solve the system using elimination. 11. x 2 − 5 x − y = 2 12. − 4 x 2 + x − 7 = y − x + y = −11 2x + 8 = − y 13. − 2 x 2 + y = 14 x + 16 14. y = x2 − 4 x + 6 − 2 x 2 − y = −14 x − 12 y = − 5 x 2 + 20 x − 12 15. A nonlinear system contains the equation of a constant function and the equation of a circle. The system has two solutions. Describe the relationship between the graphs. Copyright © Big Ideas Learning, LLC Algebra 2 79 All rights reserved. Resources by Chapter Name _________________________________________________________ Date _________ 3.5 Practice B In Exercises 1–4, solve the system by graphing. Check your solution(s). 1. y = − 2 x2 + 4 x − 3 2. y = − 3x 2 + 6 y = x2 − 2 x + 3 y = 3x y = − ( x + 3) 2 3. 4. y = 3x 2 − 6 x + 5 y = ( x − 1) + 2 2 y = x2 − 9 In Exercises 5 and 6, solve the system of nonlinear equations using the graph. 5. y 6. y 1 −2 2 5 x 2 −4 2 x In Exercises 7–10, solve the system by substitution. 7. y = x2 − 3 8. y − 12 x + 15 = 3x 2 y + 1 = − x2 3 x 2 − 16 x + 13 − y = 0 9. x 2 + y 2 = 6 10. x 2 + y 2 = 13 x + 2 y = 12 x − y = −1 In Exercises 11–14, solve the system using elimination. 11. x 2 − 3 x − y = − 6 12. y = x 2 + 3x − 8 3x − y = 5 − y = 3x − 8 13. y = − 2 x 2 − 18 x − 16 14. − 6 x 2 − y = − 32 x + 50 y = 3 x 2 + 12 x + 24 12 x 2 − y = 64 x − 76 15. A nonlinear system contains the equation of a constant function and the equation of a circle. The system has one solution. Describe the relationship between the graphs. 80 Algebra 2 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. Name _________________________________________________________ Date _________ 3.5 Puzzle Time What Do You Get When You Cross A Rocket Ship With A Potato? Write the letter of each answer in the box containing the exercise number. Solve the system by graphing, substitution, or elimination. Answers 1. y = 2 y = x 2 − 14 U. (0.5, 5.5); (1, 8) 2. y = − 2x + 1 P. (4.16, − 7.325); (− 2.16, 5.325) 2 y = − x + 10 N. (− 2, − 3); ( 43 , 11 3) 2 3. y = 4x − x + 5 y = 2 x2 + 2 x + 4 K. (− 8, − 6); (6, 8) 4. 2 x 2 − 6 x − y = −12 S. (− 4, 2); ( 4, 2) − 2 x + y = 12 D. (0, 12); (4, 20) 2 5. 3 x + 4 x − y = 7 I. no solution 2 x − y = −1 6. − x + y = 4 x2 + y = 3 7. x 2 + y 2 = 100 y − x = 2 1 2 3 4 5 6 7 82 Algebra 2 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved.