Lesson 7.2, For use with Solve the equation.
1.
6a – 3 + 2a = 13
2.
4(n + 2) – n = 11
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3. You burned 8 calories per minute on a treadmill
and 10 calories per minute on an elliptical trainer for a total of 560 calories in 60 minutes. How many minutes did you spend on each machine?
treadmill: 20 min,
ANSWE elliptical trainer: 40 min
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Daily Homework For use after 1. Use the graph to solve the linear system
3x – y = 5
–x + 3y = 5
ANSWE
(2, 1)
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Daily Homework For use after 2. Solve the linear system by graphing.
2x + y = –3 –6x + 3y = 3
ANSWE
(–1, –1)
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Daily Homework For use after 3. A pet store sells angel fish for $6 each and clown loaches for $4 each. If the pet store sold 8 fish for $36, how many of each type of fish did it sell?
ANSWE
2 angel fish and 6 clown loaches
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6
EXAMPLE 1
Use the substitution Solve the linear Equation Equation 7
EXAMPLE 2
Use the substitution method
8
for Examples 1 and 2
EXAMPLE 1
Use the substitution GUIDED PRACTICE
method
Solve the linear system using the 1.
y = 2x + 5
3x + y = 10
ANSWE (1, 7)
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for Examples 1 and 2
EXAMPLE 2
Use the substitution GUIDED PRACTICE
method
Solve the linear system using the ANSWE (0, –3)
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for Examples 1 and 2
EXAMPLE 2
Use the substitution GUIDED PRACTICE
method
Solve the linear system using the ANSWE (–2, –1)
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EXAMPLE 3 Solve a multi­step problem
WEBSIT
Many businesses pay website hosting companies to store and maintain the computer files that make up their websites. Internet service providers also offer website hosting. The costs for website hosting offered by a website 12
EXAMPLE 3 Solve a multi­step problem
SOLUTI
STEP 1
Write a system of equations. Let y be the total
Equation 1: Internet service y = 10 + 21.95 13
EXAMPLE 3 Solve a multi­step problem
Equation 2: Website hosting y = 22.45 x
The system of y = 10 + Equation y = Equation 14
EXAMPLE 3 Solve a multi­step problem
STEP 2
Substitute 22.45x for y in Equation 1 and solve
y = 10 + Write 22.45x = 10 + 0.5x = 10
x = 20
ANSWE
Substitute Subtract 21.95x from Divide each side The total cost will be the same for both 15
GUIDED PRACTICE for Example 3
4. In Example 3, what is the total cost for website hosting for each company after 20 months? ANSWE $449
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GUIDED PRACTICE for Example 3
5. WHAT IF? In Example 3, suppose the Internet service provider offers $5 off the set­up fee. After how many months will the total cost for website hosting be the same for both ANSWE
10 mo
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EXAMPLE 4 Solve a mixture problem
ANTIFREE
For extremely cold temperatures, an automobile manufacturer recommends that a 70% antifreeze and 30% water mix be used in the cooling system of a car. How many quarts of pure (100%) 18
EXAMPLE 4 Solve a mixture problem
SOLUTI
STEP 1
Write an equation for the total number of quarts and an equation for the number of quarts of antifreeze. Let x be the number of quarts of 100% antifreeze, and let y be the number of 19
EXAMPLE 4 Solve a mixture problem
Equation 1: Total number of x + y = Equation 2: Number of quarts of x quarts of
100% y quarts of
50%–50% 11 quarts of
1 x + 0.5 y = x + 0.5y = 20
EXAMPLE 4 Solve a mixture problem
The system of x + y =11Equation x + 0.5y = Equation STEP 2
Solve Equation 1 x + y = x = 11 – y
Write Revised Equation 1
STEP 3
Substitute 11 – y for x in Equation 2 and solve
Write Equation 2.
x + 0.5y = 21
EXAMPLE 4 Solve a mixture problem
(11 – y) + 0.5y y = 6.6
Substitute 11 – y for x.
Solve for y.
STEP 4
Substitute 6.6 for y in the revised Equation 1 to
find the value of x.
x = 11 – y = 11 – ANSWE
Mix 4.4 quarts of 100% antifreeze and 6.6 quarts of a 50%
antifreeze and 50% water mix to get 11 quarts of 22
GUIDED PRACTICE for Example 4
6. WHAT IF? How many quarts of 100% antifreeze and a 50% antifreeze and 50% water mix should be combined to make 16 quarts of a 70% antifreeze and 30% water ANSWE
6.4 quarts of 100% antifreeze and 9.6 quarts of a 50%
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