Exam 9: Systems of Equations

Solve. -Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Solve. -The sum of three numbers is 5. The first, minus the second, plus 2 times the third, is 0. The third, plus 4 times the first, plus the second, is -10. What are the numbers?

Solve. -The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?

Solve. -x + y + z = 7 x - y + 2z = 7 5x + y + z = 11

Classify the system as consistent or inconsistent, and dependent or independent. -4x + 4y = 1 8x + 8y = 2

Solve. -John and Tony start from GraysLake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Solve the problem. -A sum of money amounting to $3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

Solve. -A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Solve the system of equations by the elimination method. -x - 3y = -5 4x - 4y = 12

Solve the problem using the elimination method. -Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

Solve using the elimination method. -x + 6y = 26 2x + 6y = 22

Solve. -A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $6, and balcony for $4. Total for a sell-out is $82,000. If half the courtside and balcony and all endzone seats are sold, the total is $47,000. How Many of each type are there?

Solve by the substitution method. -8x + 17 = 9y -6x - 2y = 4

Classify the system as consistent or inconsistent, and dependent or independent. -x - 3y = 6 3y + 1 = x

Solve the problem. -Anne and Nancy use a metal alloy that is 16% copper to make jewelry. How many ounces of an alloy that is 10% copper must be mixed with an alloy that is 20% copper to form 55 ounces of the desired alloy?

Solve the problem. -The perimeter of a rectangle is 78 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 132 m. What are the length and width of the rectangle?

Solve the system of equations by the elimination method. -9x + 9y = -45 -4x - 6y = 20

Solve graphically. -x = -2 y = 1

Solve using the substitution method. -x + y = 16 y = 3x + 4

Solve. -x - y + 2z = -3 4x + z = 0 X + 5y + z = 15