Applications of Systems of Linear Equations

1
Applications of Systems of Linear Equations

• In Two Variables
• 3.4
• SSC 105

2

• When an application has more than one unknown, it
  may be necessary to use multiple variables.
• When two variables are present, the goal is to
  set up a system of two independent equations.
• To solve the system, use the substitution method
  or the addition method.

3

• There are several types of application problems
  that can be solved using a system of linear
  equations in two variables
• Cost applications
• Mixture applications
• Applications involving principal and interest
• Applications involving distance, rate, and time
• Geometry applications

4
Steps to Solve Applications

• Label two variables.
• Construct two equations in words.
• Write two equations.
• Solve the system.
• Write the answer.

5
Exercise 10

• At one store, 5 pairs of jeans and 2 sweatshirts
  costs 166, while 3 pairs of jeans and 4
  sweatshirts costs 164. Find the cost of one
  sweatshirt.
• A) 23
• B) 24
• C) 20
• D) 26

6
Mixture Problem Skill Prac p.211
A pharmacist needs 8 ounces (oz.) of a solution
that is 50 saline. How many ounces of 60 saline
solution and 20 saline solution must be mixed to
obtain the mixture needed?
Total ounces needed 8 X Y 8
X number of oz. of 60 saline Y number of oz.
of 20 saline
Amount of saline in resulting solution
50 X(.60) Y(.20) 8(.50)
The system of equations is
7
Answer
6 oz. of 60 solution and 2 oz. of 20 solution.
8
Principal Interest- 20 p. 216
Sonia invested a total of 12,000 into two
accounts paying 7.5 and 6 simple interest. If
her total return at the end of the first year was
840, how much did she invest in each account?
Total amount invested 12,000 X Y 12000
X amount in acct. paying 7.5 Y amount in
acct. paying 6
Total interest after one year 840 X(.075)
Y(.06) 840
The system of equations is
9
Answer

• She invested 8000 in the 7.5 account and 4000
  in the 6 account.

10
Distance, Rate, Time Skill Pr p. 213
A plane flies 1200 mi. from Orlando to New York
in 2 hr. with a tailwind. The return flight
against the same wind takes 2.5 hr. Find the
speed of the plane in still air and the speed of
the wind.
X Speed of plane Y Speed of wind
Distance (Rate)(Time)
Flight Orlando to NY Distance (Rate)(Time)
1200 (x y) (2)
Flight NY to Orlando Distance (Rate)(Time)
1200 (x - y)
(2.5)
The system of equations is
11
Answer

• The speed of the plane is 540 mph and the speed
  of the wind is 60 mph.

12
Geometry Application-ex. 5 p. 214
The sum of the two acute angles in a right
triangle is 90º. The measure of one angle is 6º
less than 2 times the measure of the other angle.
Find the measure of each angle.
Sum of two acute angles 90º X Y 90
X one acute angle Y other acute angle
One angle is 6º less than 2 times the measure of
the other angle x 2y -
6
The system of equations is
13
Answer

• The two acute angles measure 32º and 58º.