System of Equations Review
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1 Name: Date: 1. Solve the following system of equations for x: x + y = 6 x y = 2 6. Solve the following systems of equations for x: 2x + 3y = 5 4x 3y = 1 2. Solve the following system of equations algebraically and check: x 4y = 16 y = 1 x 7. Solve the following system of equations graphically and check: 3x + y = 3 y = 2x 7 3. Solve the following system of equations for x: 3x + y = 9 2x y = 6 8. Solve algebraically and check: 4x + 3y = 12 2x + y = Solve the following system of equations algebraically and check: 3x + 2y = 6 5x 3y = Solve graphically and check: 2x + y = 5 x 2y = Solve the following system of equations for x: 3x + 3y = 21 6x 3y = Solve the following system of equations graphically and check: 2x + y = 1 x + 2y = 4 page 1
2 11. Solve the following system of equations graphically and check: y = 3x 7 2x + 3y = Which ordered pair is the solution to this system of equations? 2x y = 10 x + y = 2 A. (4, 2) B. (4, 2) C. (2, 4) D. ( 4, 2) 12. Which ordered pair is the solution to this system of equations? y = x + 4 x + y = 2 A. (1, 5) B. (0, 2) C. ( 1, 3) D. ( 4, 0) 16. What is the solution for x in the following system of equations? y = 2x 3 y = x + 1 A. 2 3 B. 2 C. 4 3 D Solve the following system of equations algebraically and check: 17. When solved graphically, which system of equations will have exactly one point of intersection? 4x + 3y = 25 5x + 2y = 33 A. y = x 20 y = x + 17 C. y = 3 5 x + 12 y = 0.6x 19 B. y = 0.5x + 30 y = 0.5x 30 D. y = x + 15 y = x Solve the following system of equations graphically and check: y = 2x + 3 x 2y = On the same set of coordinate axes, graph the following system of inequalities and label the solution set S: x + y < 3 y 2x page 2
3 19. Which ordered pair is in the solution set of the system of inequalities shown in the graph? A. (0, 0) B. (1, 5) C. ( 3, 3) D. (3, 3) 22. The accompanying diagram represents the graphs of the inequalities y 3 and x < 2. Which ordered pair names a point in the solution set of this system of inequalities? A. (3, 5) B. (3, 5) C. ( 3, 5) D. ( 3, 5) 20. On the same set of coordinate axes, graph the following system of inequalities. Label the solution set S. y 2x + 4 x y < Which point is in the solution set of the system of inequalities shown in the accompanying graph? 21. Which ordered pair is in the solution set of the system of inequalities shown in the accompanying graph? A. (2, 5) B. (2, 2) C. (4, 3) D. ( 4, 3) A. (0, 4) B. (2, 4) C. ( 4, 1) D. (4, 1) page 3
4 24. Which ordered pair is in the solution set to the system of inequalities shown in the accompanying graph? 25. Graph the following systems of inequalities on the accompanying set of axes and label the solution set S: y > x 4 y + x 2 [Only a graphic solution can receive full credit.] A. (0, 0) B. (0, 1) C. (1, 5) D. (3, 2) 26. Which ordered pair is in the solution set of the following system of inequalities? y < 1 2 x + 4 y x + 1 A. ( 5, 3) B. (0, 4) C. (3, 5) D. (4, 0) page 4
5 27. Graph the following system of inequalities on the set of axes shown below and label the solution set S. y > x + 2 y 2x On the set of axes below, solve the following system of inequalities graphically. Label the solution set S. 2x + 3y < 3 y 4x The graphs of the equations x 2 + y 2 = 4 and y = 2 are drawn on the same set of axes. What is the total number of points common to both graphs? A. 1 B. 2 C. 3 D Solve the following system of equations algebraically and check. y = x 2 + 3x + 4 y x = 7 page 5
6 31. Solve the following system of equations algebraically and check: y = 3x 2 8x + 5 x + y = Solve the following system of equations algebraically or graphically for x and y: y = x 2 + 2x 1 y = 3x + 5 For an algebraic solution, show your work here. For a graphic solution, show your work here. 32. Which is a point of intersection of the graphs of y = 4 x and y = x 2 x? A. (3, 1) B. ( 1, 5) C. ( 2, 6) D. (4, 0) 33. Solve the following system of equations and check: y = x 2 4x + 3 y = 2x 2 page 6
7 35. Solve the following system of equations: y = x 2 + 4x + 1 y = 5x + 3 [The use of the grid below is optional.] 36. Solve the following system of equations algebraically or graphically for x and y: y = x 2 + 4x + 6 y = 2x + 6 y x page 7
8 37. Which ordered pair is a solution of the system of equations shown in the graph below? 38. On the set of axes below, solve the following system of equations graphically for all values of x and y. y = x 2 4x + 12 y = 2x + 4 A. ( 3, 1) B. ( 3, 5) C. (0, 1) D. (0, 4) page 8
9 39. Which graph can be used to find the solution of the following system of equations? y = x 2 + 2x + 3 2y 2x = 10 A. B. C. D. page 9
10 40. Which graph could be used to find the solution of the system of equations y = 2x + 6 and y = x 2 + 4x + 3? A. B. C. D. page 10
11 Problem-Attic format version c EducAide Software Licensed for use by David Powder Terms of Use at 05/01/ x = 4, y = 3 4. ( 2, 6) [graph] x = 6, y = 4 x = 4, y = x = 2, y = x = 3, y = C x = 7, y = x = 0, y = A B A [graph] A [graph] B C C D [task] D Both inequalities are graphed and shaded correctly, and at least one is labeled, and the solution set is labeled S. Both inequalities are graphed and shaded correctly, and at least one is labeled. The solution set is labeled S. A 30. (1, 8) and ( 3, 4) 31. (2, 1) and ( 1 3, 8 3 ) (1, 0) and (5, 8) C 34. (3, 14) and ( 2, 1) 35. ( 1, 2) and (2, 13) 36. ( 2, 2) and (0, 6) 37. B
12 Teacher s Key Page (2, 0) and ( 4, 12) A D
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Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Monday 8 May 017 Morning Time: hours Paper Reference AAL30/01 You must