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MTH-4101-2 C Equations & Inequalities II1. What is the solution of the following system of equations? Write your answer as an ordered pair. y x /52. Determine the solution set for the following system of equations: y – 4 = 3x – 1 x –3 –2 –1 0 y –6 –3 0 3 y–x=1 x –2 –1 0 1 y –1 0 1 2 /33. Without solving, express the following as a system of two equations, making sure to define your variables. If I buy 2 shirts and 3 ties, my bill comes to $213. However, if I buy 5 ties and 3 shirts my bill comes to $337. What is the price of a single shirt and tie? /5
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4. Solve the following system of equations graphically. Write your solution as an ordered pair. 1) 4y = 2 – 5x 2) 6 – 2y = 0 y x /55. Solve the following system of equations graphically. Write your solution as an ordered pair. 1) 2y + x = 0 2) 3/2x = 3 – y y x /5
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6. Using the method of your choice, determine the solution of the following system of equations; write your answer as an ordered pair: 1) 1/2x – 1/3y = 1 2) 2/3x + 1/2y = –2 /107. Using the method of your choice, determine the solution of the following system of equations; write your answer as an ordered pair: 1) x = 5y – 15 2) y = 1/5x – 1 /108. Using the method of your choice, determine the solution of the following system of equations; write your answer as an ordered pair: 1) 5x + 2y = 4x + 8 2) 4y = 20 – 3x /10
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9. During a Montreal Alouettes football game, I buy 2 hamburgers and 3 hotdogs and it costs me $8.25. The next game, I buy 4 hamburgers and 5 hotdogs for $15.25. What is the price of 1 hotdog and 1 hamburger? /910. The difference between two numbers is 9. One-sixth the smaller number added to one-third the larger number is equal to 12. What are the two numbers? /911. A brother is 5 years older than his sister. Three years from now, the sister will be three-quarters of her brother’s age then. How old are the brother and sister now? /912. Given the adjacent system of inequalities, state whether or not the following points belong to the solution set: y a) (1, 2) b) (2½, 3/4) x /4
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13. Solve the following system of inequalities graphically: 1) x + 2y ≤ 4 2) 3x – y ≥ 3 y x /814. Solve the following system of inequalities graphically: 1) x + y < 2 2) x ≥ y + 1 y x /8
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