Exam 9: Systems of Equations

Solve. -A grain dealer sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $34.70; to another, 2 of wheat, 3 of corn, and 5 of rye, for $35.00; and to a third, 3 of wheat, 5 of corn, and 2 of rye, for $38.30. What was the Price per bushel for corn?

Solve the system of equations by the elimination method. --0.8x + 0.4y = 4.8 0.1x - 0.1y = -0.7

Classify the system as consistent or inconsistent, and dependent or independent. -3x = y + 3 6x - 2y = 3

Solve. -Some people must eat a low-sodium diet with no more than 2000 mg of sodium per day. By eating 1 cracker, 1 pretzel, and 1 cookie, a person would ingest 149 mg of sodium. If a person ate 8 pretzels and 8 cookies, he or she Would ingest 936 mg of sodium. By eating 6 crackers and 7 pretzels, the person would take in 535 mg of sodium.Find the amount of sodium in each. Which of the following is true?

Solve. -A $78,000 trust is to be invested in bonds paying 7%, CDs paying 5%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $6310 annual income from the Investments, how much should the bank invest in bonds?

Solve using the elimination method. -4 x - y = 19 5x + y = 35

Solve. -x - z = -7 3x - y = -1 X + y + z = 18

Solve the problem. -The sum of two numbers is 34 and their difference is 12. Find the numbers.

Solve the problem. -A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Solve the problem using the elimination method. -The sum of two numbers is 100. The second number is three times as large as the first number. What are the numbers?

Solve the system of equations by the elimination method. -

Solve by the substitution method. -x - 5y = -27 -6x - 6y = -90

Solve graphically. -3x + 4y = 31 4x - 2y = 34

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

Solve the problem. -There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

Solve the system of equations by the elimination method. -x + 5y = 2 -4x + 6y = -8

Solve the problem. -The perimeter of a rectangle is 56 cm. One side is 12 cm longer than the other side. Find the lengths of the sides.