362 CHAPTER 6 Algebra, Graphs, and Functions 21. = + − = − y x x y 2 3 1 2 3 3 Infinite number of solutions; dependent system 22. = − + + = y x x y 3 2 2 3 2 4 Infinite number of solutions; dependent system In Exercises 23–34, solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 23. = + = − + y x y x 9 11 (1, 10) 24. = − = − y x y x 2 1 3 4 (3, 5) 25. + = − = x y x y 6 3 3 3 4 − (1, 1) 26. + = − − + = x y x y 3 4 2 5 11 ( 2, 1) − 27. − = − = y x x y 4 3 No solution; inconsistent system 28. + = + = x y y x 3 5 No solution; inconsistent system 29. = − + + = y x x y 2 3 3 3 6 (3, 1) 30. + = − = + x y x y 5 3 5 3 5 5 − (2, 5) 31. − = − = − x y y x 2 3 4 (3, 5) 32. − = − = + x y y x 1 2 4 − − ( 3, 2) 33. x y x y 3 15 1 3 5 + = = − + 34. x y x y 2 12 1 2 6 + = = − + In Exercises 35– 48, solve the system of equations by the addition method. If the system does not have a unique ordered pair as a solution, state whether the system is inconsistent or dependent. 35. + = − = x y x y 4 3 8 (3, 1) 36. − = − + = x y x y 3 1 5 3 13 (2, 1) 37. + = − − = − x y x y 4 3 1 2 13 ( 4, 5) − 38. + = + = x y x y 2 15 3 5 ( 1, 8) − 39. + = + = − x y x y 2 5 6 4 3 2 ( 2, 2) − 40. − = − = x y x y 3 2 9 9 5 24 (1, 3) − 41. − = + = − x y x y 5 2 16 4 3 1 (2, 3) − 42. + = − = − x y x y 2 3 6 5 4 8 (0, 2) 43. − = − = − x y y x 3 2 7 4 6 14 Infinite number of solutions; dependent system 44. − = − = − x y y x 2 7 17 21 6 51 Infinite number of solutions; dependent system 4. A system of equations that has at least one solution is called a(n) ________ system of equations. Consistent 5. A system of equations that has an infinite number of solutions is called a(n) ________ system of equations. Dependent 6. If the graphs of the equations in a system of linear equations are parallel lines, then the system has ________ solution(s). No 7. If the graphs of the equations in a system of linear equations intersect at only one point, then the system has ________ solution(s). One 8. If the graphs of the equations in a system of linear equations are the same line, then the system has a(n) ________ number of solutions. Infinite 9. When solving a system of linear equations, if you obtain a true statement such as 0 0 = or 6 6, = the system is dependent and has a(n) ________ number of solutions. Infinite 10. When solving a system of linear equations, if you obtain a false statement such as 4 0 = or 2 0, − = the system is inconsistent and has ________ solution. No Practice the Skills In Exercises 11 and 12, determine which ordered pairs are solutions to the given system. 11. y x4 2 (2, 6) (3, 10) (1, 7) = − − y x 8 = − + (2, 6) 12. + = − − x y2 6 ( 2, 4) (2, 2) (3, 9) x y 6 − = − ( 2, 4) − In Exercises 13–22, solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 13. y x y x 2 3 3 5 3 = + = − + (0, 3) 14. y x y x 6 2 1 3 2 = − = − − − (0, 2) 15. y x y x 3 1 = − + = − (2, 1) 16. y x y x 2 3 4 = − + = − + (1, 1) 17. x y x y 2 4 3 3 + = + = − ( 2, 3) − 18. x y x y 3 3 2 4 + = − + = − (3, 2) 19. y x x y 1 2 1 2 4 = − + + = No solution; inconsistent system 20. y x x y 1 2 2 2 6 = + − = No solution; inconsistent system Infinite number of solutions; dependent system Infinite number of solutions; dependent system
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