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Practice Problems 1 2 3 4 5 6 7 8 9 Return to MENU Practice Problems 123456789123456789

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Practice Problem #1 What is the sum of the solutions for y = x + 3 3x + y = 5 ANSWER

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Answer 1) What is the sum of the solutions for y = x + 3 3x + y = 5 Return to Practice Problems

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Practice Problem #2 Solve. Write your answer as an ordered pair. -0.5x + y = - 1 y - 1 = 2 -7x + 2 ANSWER

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Answer 2) Step 1: solve each equation for y -0.5x + y = - 1 becomes y = 0.5x - 1 y - 1 = 2 -7x + 2 becomes y = -7x +5 Step 2: solve by substitution 0.5x – 1 = -7x + 5 7.5x = 6 x = 0.8 Step 3: use y - 1 = 2 -7x + 2, substitution 0.8 for x y – 1 = 2 – 7(0.8) + 2 y = 2 – 5.6 + 2 + 1 y = -0.6 Answer: (0.8, -0.6) Return to Practice Problems

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Practice Problem #3 Solve the system. What is the sum of x and y? y = 9x + 20 y = -1/3 x + 13 ANSWER

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Answer 3) y = 9x + 20 y = -1/3 x + 13 Use substitution 9x + 20 = -1/3x + 13 +1/3x 9 1/3x + 20 = 13 Return to Practice Problems 9 1/3x + 20 = 13 -20 -20 9 1/3x = -7 9 1/3 x = -3/4 y = 9(-3/4) + 20 y = 13.25 Sum is -0.75 + 13.25 Sum is 12.5

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Practice Problem #4 Solve. What is the product of x and y? 2y = 3x + 4 y = -2x - 1.5 ANSWER

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Answer 4) Solve. What is the product of x and y? 2y = 3x + 4 y = -2x - 1.5 Answer: -0.5 Return to Practice Problems

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Practice Problem #5 Clair bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item. ANSWER

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Answer 5) Let x = price per bar of soap, y = price per sponge 3x + 5y = 2.31 5x + 3y = 3.05 x = $0.52 y = $0.15 Return to Practice Problems

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Practice Problem #6 Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast, and $.90 for one egg and one piece of toast. Write and graph a system of equations to determine how much she charges for each egg and each piece of toast. Let x represent the number of eggs and y the number of pieces of toast. ANSWER

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Answer 6) Let e = price per egg, t = price per slice of toast 2e + t = 1.50 e + t = 0.90 $0.60 per egg $0.30 for toast Return to Practice Problems

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Practice Problem #7 Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has. ANSWER

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Answer 7) Let x = 1 dollar bills, y = 5 dollar bills x + y = 14 x + 5y = 30 4 five-dollar bills 10 one-dollar bills Return to Practice Problems

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Practice Problem #8 Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for a total of $1,155.00. Find the number of adult tickets sold and the number of student tickets sold. ANSWER

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Answer 8) 6a + 4.5s = 1155 a + s = 240 50 student and 190 adult tickets Return to Practice Problems

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Practice Problem #9 Tom has a collection of 27 CDs and Nita has a collection of 18 CDs. Tom is adding 3 CDs a month to his collection while Nita is adding 6 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs. ANSWER

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Answer 9) Tom: y = 27 + 3x Nita: y = 18 + 6x 3 months Return to Practice Problems Months Number of CDs 10 20 30 40 50 1 2 3 4 5 6

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Systems of Equations & Inequalities © Beth MacDonald 2009.

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