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.