CW / HW 4-7B Solving Systems Applications with MatricesFor each problem:A. Define the variables. There may be two or three unknown variables.B. Write the system of equations. There may be two or three equations.C. Solve the system using matrices and technology. Answer appropriately.

Solve using matrices. Be sure to get in Standard Form with variables lined up!!!!

x+ y + z = 4 x + y + z = 4 Yÿ Jr'ÿ'ÿ ÿ -ÿ H

1. 4x + 5y ÿ-0ÿ= 3 2. 4x =-5ÿ+ 3 ÿ]X ÿ'ÿ] ÿ'0ÿ"-3

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3. A boat's crew rowed 16 km downstream in 2 h, but theÿrreturÿ--'n trÿ upstream took 4 h. What was the speedof the current and the boat's speed in still water?

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4. Devon has 60 coins in dimes and quarters.does she have?

The total value of the coins is $9.30. How many of each coinIll

5. A manufacturer of educational supplies makes plastic shapes to hand in the classrooms. A package of

shapes contains sq=ÿuaresr De-ntaÿnnsr and hexagons. There are 24 sÿ,ÿ in the package with a totalnumber of 112 sides. If there are 10 more squares than pentagons(findÿthe number of squares,

• . , , "ÿpenta,ÿonsÿxagons in thÿpackage.

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speed of the plane and the speed of the vÿnd.With aÿnd, a plane flew 1740 km in 6 h. With a head windÿ it flew only 570 km in 3 h. Find the

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. The perimeter of a rectangle is 178 cm. The length of the rectangle iÿs 5_cm less than the width., Find the/ength and widthÿf the rectangl--rÿ. ÿ

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8. A box of wood pieces contains wood cut into triangular, square, aÿd pentaÿgonal shapes. There are(ÿ 80 pieces of wood in the boxx, and the pieces have"--ÿ totÿ(ÿ[Ides, lÿhere are 16 more triangula'kÿ

piece_., s than square piecesÿIthe number of_pieces of wood of each shÿ)e in the'box..-- '

9. At Brownwell High School there are 281 total membÿs in the band. There are 23 more boys than girls.Write a system of equations and solve to tincl out how many are boys and how many are girls?

10. A trainload of cars and pick-up trucks is on its way to the car dealership where you work. Before theyarrive, the dealer receives an invoice showing that a total of 160 vehicles will be on the train for thedealer but the part of the invoice showing how many of each vehicle is coming has been torn off andlost. Your boss desperately needs to know how many of each is coming. The delivery invoice shows atotal mass of 183ÿ00 kilograms of vehicles and you know that each truck weighs 1400 kg and each car

1006 kg. e number of cars and trucks that arrive at the dealership.

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11. Billy Bob delivers ÿ bread, and eggs to Bubba's Camp Store. On Monday the bill foÿ,,4.,loaves of bread and 6dozen eggs w---'ass ÿ31.16. On Tuesday the bill for 5 gallons of milk, 10 loaves of bread,

nd 3 dozen- eggs was $2ÿ5. On Wednesday the bill for 2 gallons of milk, 5 loaves of bread, and 7 dozen

eggs was $18.05. Find the cost of one gallon of milk,,one loaf of bread and a one dozen eggs.

12. When she rows with the current, Mindy can row 24 mi in 3 h. Aÿainst the same current, Mindy can row only2/3 of this distance in 4 hÿ'ÿthe rate of the current and Mindy's rowing rate in still water.

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