Systems Linear and Quadratic · 2016-11-14 · Systems Linear and Quadratic Name: Date: 1. The...

Systems Linear and Quadratic

Name: Date:

1. The graphs of the equations x2 + y2 = 4 and y = 2 are drawn on the same set of axes. What is the total number ofpoints common to both graphs?

A. 1 B. 2 C. 3 D. 4

2. Solve the following system of equations algebraically and check.

x2 + y2 = 25x + 2y = 10

3. What is the solution of the following system?

(y = x2 + 3) ∧ (y = x + 3)

A. (0, 3) B. (2, 7) C. (1, 5) D. (6, 3)

4. What is the total number of points of intersection of the graphs of the equation x2 + y2 = 9 and y = x?

A. 1 B. 2 C. 3 D. 4


y = x2 + 3x + 4y − x = 7

page 1

6. Solve the following system of equations algebraically and check:

y = 3x2 − 8x + 5x + y = 3

7. Solve the following system of equations for the positive values of y:

x + y2 = 13x = −3

8. Which is a point of intersection of the graphs of y = 4 − x and y = x2 − x ?

A. (3, 1) B. (−1, 5) C. (−2, 6) D. (4, 0)

9. The graphs of the equations x2 + y2 = 9 and x = 1 are drawn on the same set of axes. What is the total number ofpoints common to both graphs?


y = 2x2 + 2x + 3x = y − 3

page 2 Systems Linear and Quadratic

11. If the graphs of x2 + y2 = 4 and y = −4 are drawn on the same axes, what is the total number of points commonto both graphs?

A. 1 B. 2 C. 3 D. 0

12. Which is a solution for the following system of equations?

y = x2

y = −2x + 15

A. (−3, 9) B. (5, 25) C. (3, 9) D. (−5, 3)

13. Solve the following system of equations and check:

y = x2 − 4x + 3y = 2x − 2

14. The graphs of the equations y = x2 and x = 2 intersect in

A. 1 point B. 2 points C. 3 points D. 0 points

15. Solve the following system of equations for the positive value of y:

x = 2y

x + y2 = 15


16. In how many points do the graphs of these functions intersect?

y = x2 − 2xy = x

A. 1 B. 2 C. 3 D. 0

17. What is the total number of points that the graph of x2 + y2 = 16 and y = x have in common?

A. 1 B. 2 C. 0 D. 4

18. Which is a point of intersection of the equations y = x and y = x2 + x − 1?

A. (0, 0) B. (1, 0) C. (−1, 0) D. (−1,−1)

19. How many points do the graphs of the equations x2 + y2 = 16 and y = x have in common?

A. 1 B. 2 C. 0 D. 4

20. The graphs of the equation y = x2 − 5x + 6 and x + y = 6 are drawn on the same set of axes. At which point do thegraphs intersect?

A. (4, 2) B. (5, 1) C. (3, 3) D. (2, 4)


21. Which is a solution for the following system of equations?

y = x2

y = −4x + 12

A. (−2, 4) B. (6, 36) C. (2, 4) D. (−6, 24)

22. Solve the following system of equations and check. [Either an algebraic or a graphic method will be accepted.]

x2 + y2 = 253x − 4y = 0

23. Which coordinate pair is a solution for the following system of equations?

x2 + y2 = 8x = 2

A. (2, 4) B. (2, 2) C. (2,√

8 ) D. (4, 2)

24. In how many points do the graphs of the equations x2 + y2 = 9 and y = 2x − 1 intersect?

A. 1 B. 2 C. 3 D. 4

25. The intersection of the graphs of the functions y = x2 and y = 2x includes the point

A. (2, 4) B. (1, 1) C. (0, 2) D. (−2, 4)



x2 + y2 = 100y = x − 2

27. Solve the following system of equations algebraically or graphically and check:

y = x2 − 6x + 5y + 7 = 2x


x2 + y2 + 4x = 0y + x = 0


y = 2x2 − 4x − 52x + y + 1 = 0

30. Solve the following system of equations for the positive value of x:

y = x

y = x2



y = x2 + 2x − 4y − 5 = 2x

32. An intersection of the graphs of the equations y = −x and y = x2 − 2 is

A. (−1,−1) B. (−2, 2) C. (2, 2) D. (1, 1)


x2 + y2 = 52x − y = −2


y = x2 − 6x + 2y + x = 2

35. Solve the following system of equations either graphically or algebraically and check.

y = x2 − 4x+92x − y + 1 =0


36. Solve the following system of equations for the positive value of x:

y = 5x + 14

y = x2

37. Solve the following system of equations graphically and check:

(x + 2)2 + (y − 1)2 = 16x − y = 1

38. If the graphs of the equations y = x + 2 and y = x2 − 3x + 6 are drawn on the same set of axes, at which point willthe graphs intersect?

A. (−2, 0) B. (1, 3) C. (1, 4) D. (2, 4)


x2 + y2 = 40y − x = 40

40. Solve the following system of equations algebraically or graphically and check.

y = x2 − 8x + 10y − x = −8


41. Solve the following system of equations graphically or algebraically and check.

y = x2 + 2x − 32x + y = −3

42. Solve this system of equations for the positive value of y.

x = 2y

x + y2 = 8


x2 + y2 = 25x = y − 1

44. Which statement describes the graphs of the equations x = −1 and x2 + y2 = 4?

A. They do not intersect.

B. They intersect in the second quadrant, only.

C. They intersect in the third quadrant, only.

D. They intersect in the second and in the third quadrants.

45. Solve the following system of equations graphically or algebraically and check:

y = −2x2 − 4x + 22x = y − 2


46. What is a solution for the system of equations y = x2 + 4 and y = x + 4?

A. (2, 8) B. (0, 4) C. (−1, 3) D. (−2, 8)

47. Solve the following system of equations graphically or algebraically and check:

x2 + y2 = 25x − y = 1

48. Which ordered pair is a solution of the system of equations y = x2 + 6 and y = x + 6?

A. (1, 6) B. (2, 8) C. (0, 6) D. (2, 10)

49. The turning point for the graph of the equation y = x2 − 2x − 3 is (1,−4). Which line does not intersect thisparabola?

A. x = 1 B. x = 3 C. y = −6 D. y = −2


y = 2x2 − 4x + 1y + 2x = 5


51. Which ordered pair is a solution for the system of equations y = x + 1 and y = x2 − 4x + 3?

A. ( 12 , 4) B. (4, 3) C. (−4,−1) D. (−4, 3)

52. If the graphs of the equation y = x2 and y = −2 are sketched on the same set of axes, the number of points ofintersection will be

A. 1 B. 2 C. 3 D. 0

53. Solve the following system of equations algebraically or graphically for x and y:

y = x2 + 2x − 1y = 3x + 5

For an algebraic solution, show your work here.

For a graphic solution, show your work here.


54. The graphs of the equations y = x2 + 4x − 1 and y + 3 = x are drawn on the same set of axes. At which point dothe graphs intersect?

A. (1, 4) B. (1,−2) C. (−2, 1) D. (−2,−5)

55. What is the total number of points of intersection in the graphs of the equations x2 + y2 = 16 and y = 4 ?

A. 1 B. 2 C. 3 D. 0

56. Solve the following system of equations algebraically.

y = x2 + 4x − 2y = 2x + 1


57. Solve the following system of equations algebraically or graphically:

x2 + y2 = 253y − 4x = 0

[The use of the accompanying grid is optional.]


58. Solve the following system of equations:

y = x2 + 4x + 1

y = 5x + 3

[The use of the grid below is optional.]

59. What is the total number of points of intersection of the graphs of the equations x2 + y2 = 16 and y = x?

A. 1 B. 2 C. 3 D. 4



y = x2 − 4x + 3y = x − 1



y = x2 + 4x + 6y = 2x + 6

�

��

�x

y

62. The graphs of the equations x2 + y2 = 4 and y = x are drawn on the same set of axes. What is the total number ofpoints of intersection?

A. 1 B. 3 C. 2 D. 0


63. Solve the following system of equations algebraically:

9x2 + y2 = 93x − y = 3

64. What is the total number of points of intersection of the graphs of the equations xy = 12 and y = −x2 + 3?

A. 1 B. 2 C. 3 D. 4

65. Solve the following system of equations algebraically.

x2 − 2y2 = 23x − 2y = 7

66. Which ordered pair is a solution to the system of equations y = x and y = x2 − 2 ?

A. (−2,−2) B. (−1, 1) C. (0, 0) D. (2, 2)

67. Which ordered pair is in the solution set of the system of equations y = −x + 1 and y = x2 + 5x + 6?

A. (−5,−1) B. (−5, 6) C. (5,−4) D. (5, 2)


68. Which ordered pair is a solution of the system of equations y = x2 − x − 20 and y = 3x − 15?

A. (−5,−30) B. (−1,−18) C. (0, 5) D. (5,−1)

69. Which ordered pair is a solution of the system of equations shown in the graph below?

A. (−3, 1) B. (−3, 5) C. (0,−1) D. (0,−4)


70. On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = −x2 − 4x + 12

y = −2x + 4


71. Which graph can be used to find the solution of the following system of equations?

y = x2 + 2x + 3

2y − 2x = 10

A. B.

C. D.


72. Which graph could be used to find the solution of the system of equations y = 2x + 6 and y = x2 + 4x + 3?

A. B.

C. D.


73. Two equations were graphed on the set of axes below. Which point is a solution of the system of equations shownon the graph?

A. (8, 9) B. (5, 0) C. (0, 3) D. (2,−3)

74. Solve the following system of equations algebraically for all values of x and y.

y = x2 + 2x − 8y = 2x + 1


75. On the set of axes below, graph the following system of equations.

y + 2x = x2 + 4y − x = 4

Using the graph, determine and state the coordinates of all points in the solution set for the system of equations.

76. How many solutions are there for the following system of equations?

y = x2 − 5x + 3y = x − 6

A. 1 B. 2 C. 3 D. 0


77. Given the system of equations:

y = x2 − 4x

x = 4

The number of points of intersection is

A. 1 B. 2 C. 3 D. 0

78. Given the equations:

y = x2 − 6x + 10y + x = 4

What is the solution to the given system of equations?

A. (2, 3) B. (3, 2) C. (2, 2) and (1, 3) D. (2, 2) and (3, 1)


79. On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = (x − 2)2 + 4

4x + 2y = 14

80. Given:

y = 14x − 3

y = x2 + 8x + 12

In which quadrant will the graphs of the given equations intersect?

A. I B. II C. III D. IV


81. What is the solution of the following system of equations?

y = (x + 3)2 − 4

y = 2x + 5

A. (0,−4) B. (−4, 0) C. (−4,−3) and (0, 5) D. (−3,−4) and (5, 0)

82. Solve the following system of equations graphically.

2x2 − 4x = y + 1x + y = 1


83. When solved graphically, what is the solution to the following system of equations?

y = x2 − 4x + 6y = x + 2

A. (1, 4) B. (4, 6) C. (1, 3) and (4, 6) D. (3, 1) and (6, 4)

84. On the set of axes below, solve the system of equations graphically and state the coordinates of all points in thesolution.

y = (x − 2)2 − 3

2y + 16 = 4x


85. On the set of axes below, solve the following system of equations graphically and state the coordinates of all pointsin the solution.

(x + 3)2 + (y − 2)2 = 25

2y + 4 = −x

86. The equations x2 + y2 = 25 and y = 5 are graphed on a set of axes. What is the solution of this system?

A. (0, 0) B. (5, 0) C. (0, 5) D. (5, 5)


87. Which graph could be used to find the solution to the following system of equations?

y = (x + 3)2 − 1x + y = 2

A. B.

C. D.

88. Solve the following system of equations algebraically:

5 = y − x

4x2 = −17x + y + 4


89. Which values of x are in the solution set of the following system of equations?

y = 3x − 6

y = x2 − x − 6

A. 0, −4 B. 0, 4 C. 6, −2 D. −6, 2

90. Which ordered pair is a solution of the system of equations shown below?

x + y = 5

(x + 3)2 + (y − 3)2 = 53

A. (2, 3) B. (5, 0) C. (−5, 10) D. (−4, 9)

91. Which ordered pair is in the solution set of the system of equations shown below?

y2 − x2 + 32 = 03y − x = 0

A. (2, 6) B. (3, 1) C. (−1,−3) D. (−6,−2)


Problem-Attic format version 4.4.218c_ 2011–2014 EducAide SoftwareLicensed for use by Clare Kerr

Terms of Use at www.problem-attic.com

Systems Linear and Quadratic 12/19/2014

1.Answer: A

2.Answer: (0, 5), (4, 3)

3.Answer: A

4.Answer: B

5.Answer: (1, 8) and (−3, 4)

6.Answer: (2, 1) and ( 1

3 ,83 )

7.Answer: 4

8.Answer: C

9.Answer: 2

10.Answer: (0, 3) and (− 1

2 ,52 )

11.Answer: D

12.Answer: C

13.Answer: (1, 0) and (5, 8)

14.Answer: A

15.Answer: 3

16.Answer: B

17.Answer: B

18.Answer: D

19.Answer: B

20.Answer: A

21.Answer: C

22.Answer: (4, 3), (−4,−3)

23.Answer: B

24.Answer: B

25.Answer: A

26.Answer: (−6,−8), (8, 6)

27.Answer: (2,−3) and (6, 5)

28.Answer: (0, 0), (−2, 2)

29.Answer: (2,−5) and (−1, 1)

30.Answer: 1

31.Answer: (3, 11), (−3,−1)

32.Answer: B

33.Answer: (4, 6), (−6,−4)

34.Answer: (0, 2), (5,−3); [graph]

35.Answer: (2, 5) and (4, 9)

36.Answer: 7

37.Answer: (−2,−3), (2, 1); [graph]

38.Answer: D

39.Answer: (−6,−2); (2, 6)

Teacher’s Key Page 2

40.Answer: (3,−5), (6,−2)

41.Answer: (0,−3), (−4, 5)

42.Answer: 2

43.Answer: (3, 4), (−4,−3)

44.Answer: D

45.Answer: (0, 2), (−3,−4)

46.Answer: B

47.Answer: (−3,−4) and (4, 3)

48.Answer: C

49.Answer: C

50.Answer: (−1, 7), (2, 1)

51.Answer: B

52.Answer: D

53.Answer: (3, 14) and (−2,−1)

54.Answer: D

55.Answer: A

56.Answer: (−3,−5) and (1, 3)

57.Answer: (3, 4) and (−3,−4)

58.Answer: (−1,−2) and (2, 13)

59.Answer: B

60.Answer: (1, 0) and (4, 3)

61.Answer: (−2, 2) and (0, 6)

62.Answer: B

63.Answer: (0,−3) and (1, 0)

64.Answer: A

65.Answer: x = 5, y = −1, and x = −19, y = −13 or

(5,−1) and (−19,−13)

66.Answer: D

67.Answer: B

68.Answer: B

69.Answer: B

70.Answer: (2, 0) and (−4, 12)

71.Answer: A

72.Answer: D

73.Answer: A

74.Answer: x = −3, y = −5 and x = 3, y = 7

75.Answer: Both equations are graphed correctly, and

(0, 4) and (3, 7) are stated.

76.Answer: A

77.Answer: A

78.Answer: D


(1, 5) is stated.

80.Answer: C

81.Answer: C

82.Answer: (2,−1); (−0.5, 1.5)

Teacher’s Key Page 3

83.Answer: C

84.Answer: Both equations are graphed correctly and

(3,−2) is stated.


(−8, 2) and (0,−2) are stated.

86.Answer: C

87.Answer: B

88.Answer: − 9

2 , 12 and 1

2 , 112

89.Answer: B

90.Answer: C

91.Answer: D

Systems Linear and Quadratic · 2016-11-14 · Systems Linear and Quadratic Name: Date: 1. The...

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Transcript of Systems Linear and Quadratic · 2016-11-14 · Systems Linear and Quadratic Name: Date: 1. The...