Kami Export - KEIRY SANDOVAL ARRIOLA - A1 Sec17-1 System Eq by Graph (2)
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School
North Hollywood Senior High *
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Course
LESSON 1-1
Subject
Mathematics
Date
May 21, 2024
Type
Pages
5
Uploaded by DoctorButterfly19758
My Notes
© 2014 College Board. All rights reserved.
Learning Targets: •
Solve a system of linear equations by graphing.
•
Interpret the solution of a system of linear equations.
SUGGESTED LEARNING STRATEGIES:
Summarizing, Paraphrasing, Marking the Text, Look for a Pattern, Create Representations
Travis Smith and his brother, Roy, are co-owners of a trucking company. The company needs to transport two truckloads of fruit grown in Pecos, Texas, to a distributing plant in Dallas, Texas. If the fruit does not get to Dallas quickly, it will spoil. The farmers offer Travis a bonus if he can get both truckloads to Dallas within 24 hours.
Due to road construction, Travis knows it will take 10 hours to drive from Pecos to Dallas. The return trip to Pecos will take only 7.5 hours. He estimates it will take 1.5 hours to load the fruit onto the truck and 1 hour to unload it.
1.
Why is it impossible for Travis to earn the bonus by himself? 2.
Travis wants to earn the bonus so he asks his brother, Roy, if he will help. With Roy’s assistance, can the brothers meet the deadline and earn the bonus? Explain why or why not.
Roy is in Dallas ready to leave for Pecos. To meet the deadline and earn the bonus, Travis will leave Pecos first and meet Roy somewhere along the interstate to give him a key to the storage area in Pecos.
3.
From Pecos to Dallas, Travis averages 45 mi/h. If Dallas is 450 mi from Pecos, write an equation that expresses Travis’s distance d
in miles from Dallas as a function of the hours h
since he left Pecos.
Solving Systems of Linear Equations
A Tale of Two Truckers
Lesson 17-1 The Graphing Method
Activity 17 • Solving Systems of Linear Equations
251
ACTIVITY 17
My Notes
© 2014 College Board. All rights reserved.
Lesson 17-1
The Graphing Method
4.
Graph the equation you wrote in Item 3.
5.
Roy leaves Dallas one-half hour before Travis leaves Pecos. In terms of the hours h
since Travis left Pecos, write an expression that represents the time since Roy left Dallas.
6.
Roy travels 60 mi/h from Dallas to Pecos. Write an equation that expresses Roy’s distance d
from Dallas as a function of the hours h
since Travis left Pecos.
7.
Graph the equation from Item 6 on the grid in Item 4.
8.
Identify the intersection point of the two lines. Describe the information these coordinates provide.
Time Since Leaving Pecos (hours)
h
d
Distance from Dallas (miles)
12
2
4
1
3
5
7
8
9
10
11
6
90
180
270
360
450
252 SpringBoard
®
Mathematics Algebra 1, Unit 3 • Extensions of Linear Concepts
continued
ACTIVITY 17
My Notes
© 2014 College Board. All rights reserved.
Lesson 17-1
The Graphing Method
You can graph each equation on a graphing calculator and use the built-in commands to determine the intersection point.
TECHNOLOGY TIP
The two equations you wrote in Items 3 and 6 form a system of linear equations
.
To determine the solution of a system of linear equations, you must identify all the ordered pairs that make both equations true. One method is to graph each equation and determine the intersection point.
9.
Graph each system of linear equations. Give each solution as an ordered pair. Check that the point of intersection is a solution of both equations by substituting the solution values into the equations.
a.
y
x
y
x
=
-
=-
+
2
10
3
5
b.
Reason abstractly.
Edgar has nine coins in his pocket. All of the coins are nickels or dimes and are worth a total of $0.55. The system shown below represents this situation. How many of each type of coin does Edgar have in his pocket? n
d
n
d
+
=
+
=
9
2
11
8
10
6
4
2
–
8
–
10
–
6
–
4
–
2
2
4
6
8
10
–
2
–
4
–
6
–
8
–
10
y
x
n
d
10
8
6
4
2
10
8
6
4
2
–
2
–
4
–
6
–
8
–
10
–
2
–
4
–
6
–
8
–
10
Two or more linear equations with the same variables form a system of linear equations.
MATH TERMS
continued
ACTIVITY 17
Activity 17 • Solving Systems of Linear Equations
253
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