5-Minute Check on Activity 3-1

1
5-Minute Check on Activity 3-1

• Examine the following graphs and determine how
  many solutions
• Solutions a) b)
  c)
• Which of the graphs above are consistent?
• Solve the systems of equations
• y 2x 1y 3x 2

One None
Infinite
Only a)
3x 2 y 2x 1 3x 2 2x 1 x 2 1
x 3 and y 3(3) 2 7
Click the mouse button or press the Space Bar to
display the answers.
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Activity 3 - 3

• Healthy Lifestyle

3
Objectives

• Solve a 2x2 linear system algebraically using
  substitution method and the addition method
• Solve equations containing parentheses

4
Vocabulary

• Addition method combining multiples of
  equations to eliminate a variable

5
Healthy Lifestyle

• You are trying to maintain a healthy lifestyle.
  You eat a well-balanced diet and exercise
  regularly. One of your favorite exercise
  activities is a combination of walking and
  jogging in your nearby park.
• One day, it takes you 1.3 hours to walk and jog a
  total of 5.5 miles in the park. You are curious
  about the amount of time you spent walking and
  the amount of time you spent jogging during the
  workout.

6
Activity Continued

• One day, it takes you 1.3 hours to walk and jog a
  total of 5.5 miles in the park.
• Write an equation using x and y, for the total
  time of your walk/jog workout in the park.
•  
•  

TT x y
7
Activity Continued

• One day, it takes you 1.3 hours to walk and jog a
  total of 5.5 miles in the park.
• 2. If you walk at 3 miles per hour, write an
  expression (not an equation) that represents the
  distance you walked.
•   
• If you jog at 5 miles per hour, write an
  expression that represents the distance you
  jogged.
• Write an equation for the total distance you
  walked/jogged in the park. 

3x
5y
D 3x 5y
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Activity Continued

• One day, it takes you 1.3 hours to walk and jog a
  total of 5.5 miles in the park.
• 5. Solve each of the equations (from 1 and 4)
  for y
• 6. Solve the system of equations from part 5
  using the substitution method for last lesson

TT x y
D 3x 5y
5.5 3x 5y 1/5(5.5 3x) y
1.3 x y
1/5(5.5 3x) y 1.3 x 5.5 3x
6.5 5x 2x 1
x 0.5 y 1.3 0.5 0.8
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Activity Continued

• Graph your equations and solve graphically
• (Window Xmin -2.5, Xmax 2.5, Ymin -2.5 and
  Ymax2.5)

10
Addition Method

• Step 1 Line up like terms in each equation
  vertically. If necessary, multiply one or both
  equations by constants so that the coefficients
  of one of the variables are opposites
• Step 2 Add the corresponding sides of the two
  equations (to eliminate a variable)
• Step 3 Solve the resulting equation for the
  remaining variable
• Step 4 Substitute the value from step 3 into
  one of the original equations and solve for the
  other variable

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Addition Example

• Solving systems of equations using addition
  method
• 3x 4y 12 and 2x
  5y 20

Step 1 3x 4y 12 2x 5y 20
Step 2 Setting up to get rid of x variables
-2 ? (3x 4y 12)
? -6x - 8y -24
3 ? (2x 5y 20) ? 6x 15y 60

7y 36
Step 3 7y 36
y 36/7 5 1/7
Step 4 3x 4(36/7) 12 3x
144/7 12
3x -60/7
x -20/7
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Problem 4

• Solving systems of equations using addition
  method
• x y 1.3 and
  3x 5y 5.5

Step 1 x y 1.3 3x 5y
5.5
Step 2 Setting up to get rid of x variables
-3 ? (x y 1.3)
? -3x - 3y -3.9
(3x 5y 5.5) ? 3x 5y
5.5
2y 1.6
Step 3 2y 1.6
y 0.8
Step 4 3x 5(0.8) 5.5 3x 4
5.5
3x 1.5 x 0.5
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Problem 5

• Solving systems of equations using addition
  method
• -2x 5y -16 and 3x
  2y 5

Step 1 -2x 5y -16 3x 2y
5
Step 2 Setting up to get rid of x variables
3 ? (-2x 5y -16)
? -6x 15y -48
2 ? ( 3x 2y 5) ? 6x 4y
10
19y -38
Step 3 19y -38
y -38/19 -2
Step 4 -2x 5(-2) -16 -2x
-10 -16
-2x -6 x 3
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Problem 6

• Solving walk/jog problem using addition method

1.3 x y
5.5 3x 5y
Step 1 3x 4y 12 2x 5y 20
Step 2 Setting up to get rid of x variables
-2 ? (3x 4y 12)
? -6x - 8y -24
3 ? (2x 5y 20) ? 6x 15y 60

7y 36
Step 3 7y 36
y 36/7 5 1/7
Step 4 3x 4(36/7) 12 3x
144/7 12
3x -60/7
x -20/7
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Summary and Homework

• Summary
• The two methods for solving a 2 x 2 system of
  linear equations algebraically
• Substitution method
• Addition method
• Homework
• pg 319 problems 1 3