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6.1 – Graphing Systems of Equations

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1 6.1 – Graphing Systems of Equations

2 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

3 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

4 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

5 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

6 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

7 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

8 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

9 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. y = -x + 1 y = x – 3 y = -x – 2

10 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

11 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

12 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

13 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

14 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

15 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

16 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

17 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. y = -x + 1 y = x – 3 y = -x – 2

18 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

19 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

20 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

21 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

22 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

23 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

24 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

25 Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 Infinite Sol. y = -x + 1 y = x – 3 y = -x – 2

26 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 y = -2x – 1

27 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2 y = -2x – 1

28 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

29 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

30 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

31 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

32 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

33 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

34 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2

35 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

36 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

37 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

38 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

39 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

40 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

41 Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1 One (0,-1)

42 b. 2x + 3y = 6 -4x – 6y = -12

43 b. 2x + 3y = 6 3y = -2x + 6 -4x – 6y = -12

44 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 -4x – 6y = -12

45 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 3 -4x – 6y = -12

46 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

47 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

48 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

49 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

50 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

51 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

52 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

53 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

54 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

55 b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12 Same line, therefore infinite sol.

56 c. 2x + y = 1 y = -2x – 1

57 c. 2x + y = 1 y = -2x + 1 m = -2, b = 1 y = -2x – 1 m = -2, b = -1 Parallel lines, therefore no sol.


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