Download Creating Systems of Linear Equations

Name ________________________________________ Date __________________ Class __________________
LESSON
12-1
Creating Systems of Linear Equations
Practice and Problem Solving: A/B
Write and solve a system of equations for each situation.
1. One week Beth bought 3 apples and 8 pears for $14.50. The next
week she bought 6 apples and 4 pears and paid $14. Find the cost of
1 apple and the cost of 1 pear.
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2. Brian bought beverages for his coworkers. One day he bought
3 lemonades and 4 iced teas for $12.00. The next day he bought
5 lemonades and 2 iced teas for $11.50. Find the cost of 1 lemonade
and 1 iced tea, to the nearest cent.
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Two campgrounds rent a campsite for one night according to the
following table. Use the table for 3–5.
Number of campers Sunnyside Campground Green Mountain Campground
1
2
3
4
$58
$66
$74
$82
$40
$50
$60
$70
3. Write the equation for the rate charged by Sunnyside Campground.
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4. Write the equation for the rate charged by Green Mountain.
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5. Solve the system of the equations you found in Problems 3 and 4. For
how many campers do the campgrounds charge the same rate? What
is the rate charged for that number of campers?
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Use the graph for 6–8.
6. Write the functions represented by the graph.
7. What does each function represent? What does the variable
represent?
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8. Solve the system of equations. Is the intersection point
shown on the graph correct?
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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2. 4 x + y + 2z = 10
Practice and Problem Solving:
Modified
−( x + y − 6z = −23.5)
1. 2nd; 3 or −3
2 x + 3 y + 3z = 13
−3( x + y − 6z = −23.5)
3 x + 8z = 33.5
− x + 21z = 83.5
st
2. 1 ; 2 or −2
3 x + 8z = 33.5
3. 1st; 4 or −4
x = 0.5
+ 3( − x + 21z = 84.5)
4. 2nd; 4 or −4
71z = 284
z=4
5. (2, 3)
6. (−6, 4)
7. (4, −1)
x + y − 6z = −23.5
8. (2, 0)
0.5 + y − 6(4) = −23.5
y =0
9. One hot chocolate is $1.
10. 9 two-point shots and 3 three-point shots
MODULE 12 Modeling with
Linear Systems
1. Multiply the first equation by 3 and the
second equation by 5 to get common
coefficients of −15.
LESSON 12-1
⎧ 4(9x − 10y = 7) ⎧36x − 40y = 28
2. ⎨
⇒⎨
⎩5(5x + 8y = 31)
⎩25x + 40y = 155
3. (1, −3)
Practice and Problem Solving: A/B
1. apple: $1.50, pear $1.25
4. (10, −10)
2. lemonade: $1.57, iced tea: $1.82
Success for English Learners
3. y = 8x + 50
1. The y-variable is eliminated.
4. y = 10x + 30
2. Multiply the equation by −3 so that the
y-variable is eliminated.
5. The camp grounds will both charge $130
for 10 campers.
6. g(t) = 2t + 4, h(t) = 2.5t + 2
MODULE 11 Challenge
x + y + z = 12
+(3 x + y − z = 32)
4 x + 2y = 44
4 x + 2y = 44
−(6 x + 2y = 56)
7. The functions represent the rates charged
by 2 different dog walkers. The variable
represents the number of dogs.
3 x + y − z = 32
+(3 x + y + z = 24)
6 x + 2y = 56
8. Yes
Practice and Problem Solving: C
4(6) + 2y = 44
y = 10
1. y =
− 2 x = −12
1
x
2
2. Sample answer: The number of bales of
hay needed to feed 3 elephants.
x=6
6 + 10 + z = 12
Solution: (0.5, 0, 4)
The solution checks in all three equations.
Reading Strategies
1.
3 x + 8(4) = 33.5
3. Sample answer: Let x = number of bales
of hay; Let y = the number of elephants;
1
+ 1, y = x − 3
(6, 3); y =
3x
Solution: (6, 10, −4)
z = −4
The solution checks in all three equations.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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