Chapter 8 Section3

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Chapter 8 Section3

• Applications of Systems of Equations in Two
  Variables

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Rest of the Homework

• Read section 8.3. Do 3, 7, 21, 25, 27, 31, 35,
  37. Be sure to follow the five-step process for
  application problems as shown in Examples 1-7.
  More details on the five-step process are given
  in section 2.5.

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Basic Problem

• In these applications we will be modeling a
  situation using a system of linear equations in 2
  variables. The most basic ones just explicitly
  give you both equations.

4

• Example
• The sum of two numbers is -42. The first number
  minus the second number is 52. What are the
  numbers?
• Step 1 What is the question? What are the
  numbers? Define the variables.
• Let x first number.
• Let y second number

5

• Step 2Translate to Algebrax y -42
• x - y 52
• Step 3 Solve the Equation(s)
• Well use the elimination method

6

• Step 4 Look BackDoes our answer appear to be
  reasonable?
• Step 5 State Your Solution
• The first number is 5 and the second is -47

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Basic Concept Total Value or Mixture

• There are typically two basic styles of equations
  in applications of linear systems. The first
  equation gives the count of items. The second
  give the value of the items.
• Examples If you have six 20 bills, what is the
  value os the money? If you have 17 gallons of 4
  milk (whole milk), how many gallons of milk fat
  do you have?

8

• Muddy Waters coffee house sells Kenyan dark roast
  for 9.00 per pound and Sumatran for 8.00 per
  pound. How many pounds of each should be used to
  make a blend that will sell for 8.40 per pound?
• What is the Question?
• Translate (use a table)
• Solve
• Look Back
• State the Solution

9

• The Academic Vice President is nearing retirement
  and made investments last year totaling 15,000.
  The yield, in simple interest, from the 2
  accounts invested in was 1,432. One account paid
  9 while the other paid 10. How much did he
  invest in each account?
• What is the Question?
• Translate (use a table)
• Solve
• Look Back
• State the Solution

10

• The perimeter of an oceanfront lot is 190m. The
  width is one-forth of the length. Find the
  dimensions of the lot (assuming it is a
  rectangle).
• What is the Question?
• Translate (use a drawing)
• Solve
• Look Back
• State the Solution

11

• Mias motorboat took 3 hr to make a trip
  downstream with a 6-mph current. The return trip
  (against the current) took 5 hr. What is the
  speed of the boat in still water?
• What is the Question?
• Translate (use a drawing and a table)
• Solve
• Look Back
• State the Solution

12

• The milk stop train leaves Redding and travels
  north towards Portland at a speed of 75 kph. Two
  hours later the express train leaves on the same
  track north and travels at 125 kph. How far from
  the station will the first train have to pull
  over on a side-track and let the second pass?
• What is the Question?
• Translate (use a drawing and a table)
• Solve
• Look Back
• State the Solution

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Group Quiz

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