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Unit 3 Exam –Systems of Equations Name: ______________________ PART I: MULTIPLE CHOICE What point is the intersection of the graphs of the lines 2x – y = 3 and x + y = 3? (1) (2,1) (3) (3,0) (2) (1,2) (4) (3,3) 1. Which ordered pair satisfies the system of equations x – y = 5 and x + y = 7? (1) (6,1) (3) (6, –1) (2) (1,6) (4) (7,2) 2. What is the solution of the following system of equations? x + 2y = 12 x–y=6 3. (1) (8,1) (2) (8,2) (3) (10,4) (4) (10, –2) What is the value of the y-coordinate of the solution to the system of equations x 2 y 9 and x y 3? (1) 6 (2) 2 4. (3) 3 (4) 5 Solve -x + y = -6 2x + 3y = 22 5. (1) (8,2) (2) (2,8) (3) (–8,2) (4) (2, –8) What is the solution of the following system of equations? 7x + y = 10 3x + y = 2 6. (1) (–4,2) (2) (2,8) (3) (2,4) (4) (2, –4) Maria went to the store and bought peanut butter cups and coffee. It cost $1.50 for 10 peanut butter cups and 2 coffees. Alexis also went to the store. It cost her $1.50 for 20 peanut butter cups and 1 coffee. How much does one cup of coffee cost? 7. (1) $0.50 (2) $0.10 (3) $0.25 (4) $50 The accompanying diagram shows the graph of a linear and a quadratic equation. How many solutions are there to this system of equations? 8. (1) 0 (2) 1 (3) 3 (4) 2 PART II: FREE RESPONSE 9. Which ordered pair satisfies the system of equations below? 3x – y = 10 x+y=2 10. What is the solution of the following system of equations? 3x + 2y = 4 –2x + 2y = 24 11. Solve the following system of equations algebraically: 3x 2 y 4 4 x 3y 7 [Only an algebraic solution can receive full credit.] 12. Write an inequality to represent the following statement. The flight to Mexico costs less than $700. 13. Graph the inequality y > x + 2 on the grid below. 14. The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90. What is the cost of each item? Include appropriate units in your answer. 15. Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza? 16. Graph the following line on the coordinate plane below. y = ½x – 3 17. Find the solution of this system of equations graphically. State and label the solution. 1 x2 2 y = -x + 5 y= 18. On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set. y = x2 + 4x – 5 y =x–1 EXTRA CREDIT The sum of two numbers is 47, and their difference is 15. What is the larger number? (1) 16 (3) 32 (2) 31 (4) 36