algebra 1 notes lesson 7-1 graphing systems of equations
TRANSCRIPT
![Page 1: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/1.jpg)
Algebra 1 Notes
Lesson 7-1
Graphing Systems of Equations
![Page 2: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/2.jpg)
Mathematics Standards- Patterns, Functions and Algebra: Generalize
patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations.
- Patterns, Functions and Algebra: Describe problem situations by using tabular, graphical, and symbolic representations.
- Patterns, Functions and Algebra: Demonstrate the relationship among zeros of a function, roots of equations and solutions of equations graphically and in words.
![Page 3: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/3.jpg)
Mathematics Standards- Patterns, Functions and Algebra: Solve real-
world problems that can be modeled using linear, quadratic, exponential or square root functions.
- Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
- Patterns, Functions and Algebra: Solve real-world problems that can be modeled using systems of linear equations and inequalities.
![Page 4: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/4.jpg)
Vocabulary
System of Equations – Two or more equations together
Ex/ 2x + 3y = 5
y = -4x + 6
Solution to Systems – Ordered pair that makes both equation true
Three possibilities
![Page 5: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/5.jpg)
Vocabulary
System of Equations – Two or more equations together
1)Exactly one solution – equations make intersecting lines
![Page 6: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/6.jpg)
Vocabulary
System of Equations – Two or more equations together
1)Exactly one solution – equations make intersecting lines
The one solution is
where the lines intersection. (x,y)
![Page 7: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/7.jpg)
Vocabulary
System of Equations – Two or more equations together
2) Infinitely many solutions – equations make the same line
![Page 8: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/8.jpg)
Vocabulary
System of Equations – Two or more equations together
2) Infinitely many solutions – equations make the same line
“Infinitely many solutions”
![Page 9: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/9.jpg)
Vocabulary
System of Equations – Two or more equations together
3) No solutions – equations make lines that DON’T intersect (parallel)
![Page 10: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/10.jpg)
Vocabulary
System of Equations – Two or more equations together
3) No solutions – equations make lines that DON’T intersect (parallel)
“No solutions”
![Page 11: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/11.jpg)
Work the next two examples on your own paper
![Page 12: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/12.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 13: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/13.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 14: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/14.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 15: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/15.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 16: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/16.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 17: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/17.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 18: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/18.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7
![Page 19: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/19.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
intersection
![Page 20: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/20.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
intersection
![Page 21: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/21.jpg)
Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
Intersection (3,5)
![Page 22: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/22.jpg)
Example 2
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
x – 2y = 4
x – 2y = -2
![Page 23: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/23.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x
-2y = 4 – x
-2 -2
y = -2 + ½x
y = ½x – 2
![Page 24: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/24.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x – x – x
-2y = 4 – x
-2 -2
y = -2 + ½x
y = ½x – 2
![Page 25: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/25.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x – x – x
-2y = 4 – x -2y = -2 – x
-2 -2
y = -2 + ½x
y = ½x – 2
![Page 26: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/26.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x – x – x
-2y = 4 – x -2y = -2 – x
-2 -2 -2 -2
y = -2 + ½x
y = ½x – 2
![Page 27: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/27.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x – x – x
-2y = 4 – x -2y = -2 – x
-2 -2 -2 -2
y = -2 + ½x y = 1 + ½x
y = ½x – 2
![Page 28: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/28.jpg)
Example 2
x – 2y = 4 x – 2y = -2
– x – x – x – x
-2y = 4 – x -2y = -2 – x
-2 -2 -2 -2
y = -2 + ½x y = 1 + ½x
y = ½x – 2 y = ½x + 1
![Page 29: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/29.jpg)
Example 2
y = ½x – 2 y = ½x + 1
No Solution
![Page 30: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/30.jpg)
Now go back to the guided notes
![Page 31: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/31.jpg)
Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X –
Y -
![Page 32: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/32.jpg)
Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X – ride time
Y -
![Page 33: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/33.jpg)
Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X – ride time
Y - walk time
x + y = 3
12x + 4y = 20
![Page 34: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/34.jpg)
Story Problemx + y = 3 12x + 4y = 20
– x – x
y = -x + 3
![Page 35: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/35.jpg)
Story Problemx + y = 3 12x + 4y = 20
– x – x – 12x – 12x
y = -x + 3
![Page 36: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/36.jpg)
Story Problemx + y = 3 12x + 4y = 20
– x – x – 12x – 12x
y = -x + 3 4y = -12x + 20
![Page 37: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/37.jpg)
Story Problemx + y = 3 12x + 4y = 20
– x – x – 12x – 12x
y = -x + 3 4y = -12x + 20
4 4
y = -3x + 5
![Page 38: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/38.jpg)
Story Problemy = -x + 3 y = -3x + 5
x = hoursrode
y = hours
walked
They walked for 2 hours.
They rode for 1 hour.
(1, 2)
![Page 39: Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e585503460f94b51cbf/html5/thumbnails/39.jpg)
Homework
Pgs. 372
16-40 (evens) 41-45 (all)