258 Chapter 3 Systems of Linear Equations and Inequalities Section 3.3 Practice Exercises Vocabulary and Key Concepts 1. a. By what nonzero constant would the second equation be multiplied to eliminate the x variable from the system of equations? 3x 4y 8 x 5y 2 b. By what nonzero constant would the first equation be multiplied to eliminate the y variable from the system of equations? 8x 5y 12 Review Exercises For Exercises 2–4, use the slope-intercept form of the lines to determine the number of solutions for the system of equations. 1 2 2. 3. 4. y y 2.32x 8.1 4x y 7 y 1.46x 8.1 2y 8x 14 y 1 2 x 4 x 1 Concept 1: The Addition Method For Exercises 5–16, solve the system by using the addition method. (See Examples 1–3.) 5. 6. 7. 8. 3x y 1 5x 2y 15 2x 3y 3 2x 5y 7 3x 4y 14 3x 2y 7 10x 2y 32 3x 10y 13 9. 10. 11. 12. 3x 7y 20 6x 9y 15 3x 10y 13 5x 6y 4 5x 3y 84 5x 2y 40 7y 4x 11 5y 1 3x 13. 14. 15. 16. 1.2x 0.6y 3 1.8x 0.8y 1.4 3x 2 4y 2 4y 3 2x 3 0.8x 1.4y 3 1.2x 0.6y 1.2 7x 3y 5y 3x Concept 2: Solving Inconsistent Systems and Systems of Dependent Equations For Exercises 17–24, solve the system. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. (See Examples 4–5.) 17. 3x 2y 1 18. 3x y 4 19. 6y 14 4x 20. 2x 4 y 6x 4y 2 6x 2y 8 2x 3y 7 y 2x 2 1 2 21. 22. 23. 24. x 1 2 x 2y 4.5 y 3 6x 1 2y 3y 2x 1 x y 0.2x 0.1y1.2 7 6 12x 4y 2 10x 15y 5 3x y 8
miller_intermediate_algebra_4e_ch1_3
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