Algebra Unit 6 Test review white boards notea.notebook. February 02, y = y = a) (-3, -2) b) (1, -3) c) (0, -1) c) (2, 3) a) ( 1, 3) d) ( 3, 1)

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1 Unit 6 white board review 1. Find the solution to the graph on the right. ( 1, 3) (3, 1) c) (2, 3) d) ( 3, 1) Graph and find the point of intersection for each. 2. (-3, -2) (1, -3) c) (0, -1) 3. Graph and find the point of intersection for each. y = y = Randy has $400 in his account, and he will deposit an additional $100 each week. Karin has $100, and she will add $200 more each week. Write two equations to represent the situation. y = -4x + 4 y = 2x + 3 y = 4x - 4 y = 2x + 3 c) y = 4x - 4 y = 1 x Graph both equations and determine when they have the same amount of money. (2, 4) (2, 2) c) no solution 1

2 4. Identify the first step to solving the system by substitution. Solve each system by substitution. substitute 2y 6 for x combine like terms c) distribute 5 d) use inverse operations to solve 5. (4, 3) (3, 7) c) (7, 3) d) ( 4, 0) Solve each system by substitution. 6. (10, 30) (2, 5) c) (2, 6) d) ( 10, 30) SET UP and SOLVE. 7. Break Even Problem. You have opened your own boat shop. Your cost to open and equip your shop was $15,000. If every boat costs you $2,500 to make and you sell them for $5,650 each, how many boats must you sell before you break even? x = Cost = Revenue = 4 boats 5 boats c) 2 boats d) 3 boats 2

3 Solve each system by adding or subtracting. 8. Solve each system by adding or subtracting. 9. ( 4, 7) ( 2, 3) (7, 4) (3, 2) c) (4, 7) c) (2, 3) d) (7, 4) d) ( 3, 2) 10. To solve this system of equations by the elimination method, what would be your first step? EXPLAIN your reasoning. c) Multiply the top equation by 3 to cancel out the x's d) Multiply the top equation by 3 to cancel out the x's Multiply the top equation by 2 to cancel out the y's Multiply the top equation by 2 to cancel out the y's 11. ( 1, 2) (2, 1) c) (1, 2) d) (2, 1) 3

4 many solutions (1, 5) no solution c) (10, 14) d) ( 11, 10) (5, 1) c) ( 5, 1) d) (1, 5) 14. ( 3, 3) 15. The sum of two number is 25. The difference of the numbers is 10. Find the two numbers. (Set up but do NOT solve.) x = one # y = another # (3, 3) c) (2, 3) d) (1, 3) 4

5 16. At a county fair, the cost for 5 slices of pizza and 4 orders of French fries is $ The cost of 2 slices of pizza and 1 orders of French fries is $ Write a system of equations to model this situation. (Set up but do NOT solve.) p = $ for 1 pizza slice f = $ for order of fries 17. There were 80 Algebra 1 students at Harlem High School, some are girls and some are boys. The ratio of girls to boys is 5 to 7. Find the number of girls and the number of boys enrolled in Algebra. (Set up but do NOT solve.) g = # of girls b = # of boys 5p + 4f = p + 1f = c) 4p + 5f = p + 2f = g + b = 80 5g = 7b c) g + b = 80 7g = 5b 4p + 5f = d) 5p + 4f = p + 2f = p + 1f = g + 7b = 80 d) 7g + 5b = 80 5g = 7b 7g = 5b 18. Four times a number plus two times another number equals 18. The sum of the two numbers is 15. Write a system of equations to model this situation. (Set up but do NOT solve.) x = one # y = another # x + y = 18 c) 4x + 2y = 18 4x + 2y = 15 x + y = Given the graph at the right, which point below is NOT a solution? ( 2, 3) (1, 2) c) (3, 1) d) (2, 3) x + y = 15 x + 2y = 18 d) x + y = 15 4x + y = 18 5

6 20. Which system is graphed at the right? Graph the solution to these systems of inequalities. 21. c) Graph the solution to these systems of inequalities. 22. c) 23. The high school is putting on a play. The maximum number of seats in the auditorium is 600 seats. The school hopes to make at least $3100. Student tickets will cost $3 each and adult tickets will cost $8 each. Write a system of inequalities to model this situation. (Set up but do NOT solve.) a + s < 600 3a + 8s < 3100 a = # of adult tickets s = # of student tickets c) a + s > 600 8a + 3s < 3100 a + s < 600 8a + 3s > 3100 d) a + s > 600 3a + 8s <

7 Solve these systems of equations using matrices. 24. ( 4, 1) Solve these systems of equations using matrices. (1, 4) c) (0, 4) d) (1, 0) 25. (7, 6) (6, 7) c) (0, 6) d) (7, 0) Solve these systems of equations using matrices. 26. ( 2, 7) (7, 10) c) ( 2, 7, 10) d) (10, 7, 2) 7

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