9.3 systems of linear equations and problem solving bobsmathclass.com copyright © 2010 all rights...

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9.3 Systems of Linear Equations and Problem Solving

BobsMathClass.Com Copyright © 2010 All Rights Reserved.

Applications of Linear Systems of EquationsMany problems involve more than one unknown quantity. Although some problems with two unknowns can be solved using just one variable, many times it is easier to use two variables. To solve a problem with two unknowns, we write two equations that relate the unknown quantities. The system formed by the pair of equations then can be solved using the previous methods.

Procedure: Solving an Applied Problem by Writing a System of EquationsStep 1. Determine what you are to find. Assign a variable for each unknown and write down what it represents.

Step 2. Write down other information. If appropriate, draw a figure or a diagram and label it using the variables from Step 1. Use a chart or a box to

summarize the information.

Step 3. Write a system of equations. Write as many equations as there are unknowns.

Step 4. Solve the system.

Step 5. Answer the question(s). Be sure you have answered all questions posed.

Step 6. Check. Check your solutions in the original problem. Be sure your answer makes sense.

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Solution:

Example 1. Solve by using a system of equations:

The sum of two numbers is 37 and their difference is –3.

x y 37x y 3

Then use either method to solve the system

Answer: The two numbers are 17 and 20. Their sum is 37 and their difference is –3.

Let x = first number and let y = second number

We need two equations with two unknowns.

2x 34x 17

17 y 37 y 20

Your Turn Problem #11

Solve by using a system of equations:

The sum of two numbers is 51 and their difference is 15.

Answer: The two numbers are 33 and 18.

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Solution:


Laura and Tony are planning to move and need to buy some cardboard boxes. At Smart and Final, they can buy either 10 small and 12 medium boxes fro $42, or 5 small and 10 medium boxes for $29. Find the cost of each size box.

10x 12y 42 5x 10y 29

Then use either method to solve the system

Answer: The cost of a small box is $1.80 and the cost of a medium box is $2.00.

Let x = cost of a small box and let y = cost of a medium box


8y 161 y 2

10x 12y 42-10x 20y -58

x 1.8

5x 10(2) 29

5x 9Your Turn Problem #2


At the Rancho Nut Ranch, 5 pounds of peanuts and 6 pounds of cashews cost $70, and 3 pounds of peanuts and 7 pounds of cashews cost $76. Find the prices charged by the ranch for a pound of peanuts and a pound of cashews.

Answer: Peanuts are $2.00 per poundCashews are $10.00 per pound

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Tickets to a play at Cucamonga Jr. High cost $2.50 for general admission and $2.00 with a student identification. If 92 people paid to see a performance and $203 was collected, how many of each type of admission were sold?Solution:

x y 922.50x 2.00y 203

Let’s use substitution.

Answer: # of generals admission = 38# of students = 54

Let x = number of general admission tickets soldlet y = number of student tickets sold


x 38x 92 54

y 54

x 92 y

(92 y2.50 2) .00y 203 230 2.50y 2.00y 203

.50y 27

Your Turn Problem #3


On a 10-day trip Dan rented a car for $31 a day at weekend rates and $40 a day at weekday rates. If his rental bill was $364, how many days did he rent a each rate?

Answer: Dan rented the car for 4 weekend days and 6 weekdays.

The End.B.R.1-15-07

9.3 systems of linear equations and problem solving bobsmathclass.com copyright © 2010 all rights...

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