1. MS Algebra A-F-IF-7 – Ch. 7.1 Solve Linear Systems by Graphing
Mr. Deyo
Solve Linear Systems by Graphing

2. By the end of the period, I will solve linear systems by graphing.
Title: 7.1 Solve Linear Systems by Graphing
Date:
Learning Target
By the end of the period, I will solve linear systems by graphing.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 7.1 Pg ) Section ______
TxtBk.Prob.#3,5,15,23,31,35 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Daily Warm-Up Exercises
For use with pages xxx–xxx
It takes 3 hours to repair a bicycle and 2 hours to make a skateboard. You spend 16 hours doing work. What are 2 possible numbers of bicycles you repaired and skateboards you made?
Graph the equation
-2x + y = 1

6. Daily Warm-Up Exercises
For use with pages xxx–xxx
It takes 3 hours to repair a bicycle and 2 hours to make a skateboard. You spend 16 hours doing work. What are 2 possible numbers of bicycles you repaired and skateboards you made?
Graph the equation
-2x + y = 1
ANSWER
ANSWER
2 bicycles and 5 skateboards, or 4 bicycles and 2 skateboards

7. Vocabulary System of Linear Equations
Solution to a System of Equations
Solve by Graphing
Solve by Elimination
Solve by Substitution

8. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

9. System of Linear Equations
Notes:
A system of equations (linear system) has two or more linear equations with the same variables.
Equation 1: y = -x + 5
Equation 2: y = ½ x + 2
solution
A solution to the system is an ordered pair ( x, y ) that is a solution to EACH of the equations (where the lines intersect).
(2, 3)

10. Problem A
Check the intersection point
Use the graph to solve the system. Then check your solution algebraically. Is (3, 2) a solution to the system?
x + 2y = 7
3x - 2y = 5

11. x + 2y = 7 (3) + 2(2) = 7 3 + 4 = 7 7 = 7 3x - 2y = 5 3(3) -2(2) = 5
Problem A
Check the intersection point
SOLUTION
Use the graph to solve the system. Then check your solution algebraically. Is (3, 2) a solution to the system?
x + 2y = 7
(3) + 2(2) = 7
3 + 4 = 7
7 = 7
3x - 2y = 5
3(3) -2(2) = 5
9 – 4 = 5
5 = 5
YES, it is a solution of the linear system because the ordered pair (3, 2) is a solution of each equation.

12. -x + 2y = 3 2x + y = 4 Is (1, 2) a solution to the system?
Problem B
Check the intersection point
Check your solution algebraically.
Is (1, 2) a solution to the system?
-x + 2y = 3
2x + y = 4

13. -x + 2y = 3 -(1) + 2(2) = 3 -1 + 4 = 3 3 = 3 2x + y = 4 2(1) + (2) = 4
Problem B
Check the intersection point
SOLUTION
Check your solution algebraically.
Is (1, 2) a solution to the system?
-x + 2y = 3
-(1) + 2(2) = 3
= 3
3 = 3
2x + y = 4
2(1) + (2) = 4
2 + 2 = 4
4 = 4
YES, it is a solution of the linear system because the ordered pair (1, 2) is a solution of each equation.
-x + 2y = 3
solution
(1, 2)
2x + y = 4
y = (1/2) x + (3/2)
y = -2x + 4

14. Storm Check (Think, Write, Discuss, Report)
What do you have to do to check that a given ordered pair is a solution for the system of equations?
To check if a given ordered pair is a solution for
the system of equations, I have to ____________
___________________________________________
__________________________________________.

15. Solve the System of Equations:
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Problem A
Step 2: Find coordinates of the point of intersection
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: -x + y = Eq. 2: x + 4y = -8
STEP 1
Graph both
equations
STEP 2
Find intersection.
STEP 3
Check solution
Eq. 1: -x + y = Eq. 2: x + 4y = -8

16. y = -(1/4)x -2 y = x -7 4y = -x -8 -(4) + (-3) = -7 4 + 4(-3) = -8
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Problem A
Step 2: Find coordinates of the point of intersection
SOLUTION
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: -x + y = Eq. 2: x + 4y = -8
STEP 1
Graph both
equations
y = x -7
y = mx + b
4y = -x -8
y = -(1/4)x -2
y = mx + b
STEP 2
(4, -3)
Find intersection.
STEP 3
Check solution
Eq. 1: -x + y = Eq. 2: x + 4y = -8
-(4) + (-3) = -7
-4 – 3 = -7
-7 = -7
4 + 4(-3) = -8
4 – 12 = -8
-8 = -8

17. Solve the System of Equations:
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Problem B
Step 2: Find coordinates of the point of intersection
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: -5x + y = Eq. 2: 5x + y = 10
STEP 1
Graph both
equations
STEP 2
Find intersection.
STEP 3
Check solution
Eq. 1: -5x + y = Eq. 2: 5x + y = 10

18. y = 5x + 0 y = -5x + 10 -5(1) + (5) = 0 5(1) + (5) = 10 -5 + 5 = 0
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Problem B
Step 2: Find coordinates of the point of intersection
SOLUTION
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: -5x + y = Eq. 2: 5x + y = 10
STEP 1
Graph both
equations
y = 5x + 0
y = mx + b
y = -5x + 10
y = mx + b
STEP 2
Find intersection.
(1, 5)
STEP 3
Check solution
Eq. 1: -5x + y = Eq. 2: 5x + y = 10
-5(1) + (5) = 0
= 0
0 = 0
5(1) + (5) = 10
5 + 5 = 10
10 = 10

19. Storm Check (Think, Write, Discuss, Report)
When you look at a graph of a system of linear equations, where do you see the solution?
When I look at a graph of a system of linear
equations, I can see the solution ______________
___________________________________________.

20. RENTAL BUSINESS Problem A
Solve a multi-step problem
RENTAL BUSINESS
A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $ 450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system.
STEP 2 Graph both equations.
STEP 3 Estimate point of intersection.
STEP 4
Check solution

21. RENTAL BUSINESS Problem A
Solve a multi-step problem
RENTAL BUSINESS
A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $ 450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system.
STEP 2 Graph both equations.
STEP 3 Estimate point of intersection.
STEP 4
Check solution

22. x + y = 25 Rentals 15x + 30y = 450 Money Collected
Problem A
Solve a multi-step problem
RENTAL BUSINESS
SOLUTION
A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $ 450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented.
x + y = 25 Rentals
15x + 30y = 450 Money Collected
STEP 2 Graph both equations.
(20, 5)
(20, 5)
STEP 3 Estimate the point of intersection.
STEP 4
Check solution
x + y = x + 30y = 450
(20) + (5) = (20) + 30(5) = 450
25 = = 450

23. WHAT IF? RENTAL BUSINESS Problem B
Solve a multi-step problem
RENTAL BUSINESS
WHAT IF?
A business rents in-line skates and bicycles. During one day, the business has a total of 18 rentals and collects $ 390 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system.
STEP 2 Graph both equations.
STEP 3 Estimate point of intersection.
STEP 4
Check solution

24. WHAT IF? RENTAL BUSINESS Problem B
Solve a multi-step problem
RENTAL BUSINESS
WHAT IF?
A business rents in-line skates and bicycles. During one day, the business has a total of 18 rentals and collects $ 390 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system.
STEP 2 Graph both equations.
STEP 3 Estimate point of intersection.
STEP 4
Check solution

25. x + y = 18 Rentals 15x + 30y = 390 Money Collected
Problem B
Solve a multi-step problem
RENTAL BUSINESS
WHAT IF?
SOLUTION
A business rents in-line skates and bicycles. During one day, the business has a total of 18 rentals and collects $ 390 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
STEP 1
Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented.
x + y = 18 Rentals
15x + 30y = 390 Money Collected
(10, 8)
STEP 2 Graph both equations.
(10, 8)
STEP 3 Estimate the point of intersection.
y = -x + 18
y = -(1/2)x + 13
STEP 4
Check solution
x + y = x + 30y = 390
(10) + (8) = (10) + 30(8) = 390
18 = = 390

26. Vocabulary System of Linear Equations
Solution to a System of Equations
Solve by Graphing
Solve by Elimination
Solve by Substitution

27. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 7.1 Pg ) Section ______
TxtBk.Prob.#3,5,15,23,31,35 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

28. By the end of the period, I will solve linear systems by graphing
Title: 7.1 Solve Linear Systems by Graphing
Date:
Learning Target
By the end of the period, I will solve linear systems by graphing
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

29. Solve the System of Equations:
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Ticket Out
Step 2: Find coordinates of the point of intersection
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: x – y = Eq. 2: 3x + y = 3
STEP 1
Graph both
equations
STEP 2
Find intersection.
STEP 3
Check solution
Eq. 1: x – y = Eq. 2: 3x + y = 3

30. -y = -x + 5 y = x - 5 y = -3x + 3 (2) - (-3) = 5 3(2) + (-3) = 3
Use the Graph and Check Method
Step 1: Graph Both Equations in the same plane
Ticket Out
Step 2: Find coordinates of the point of intersection
SOLUTION
Step 3: Check each equation to verify solution
Solve the System of Equations:
Eq. 1: x – y = Eq. 2: 3x + y = 3
STEP 1
Graph both
equations
-y = -x + 5
y = x - 5
y = mx + b
y = -3x + 3
y = mx + b
STEP 2
Find intersection.
STEP 3
Check solution
Eq. 1: x – y = Eq. 2: 3x + y = 3
(2) - (-3) = 5
2 + 3 = 5
5 = 5
(2, -3)
3(2) + (-3) = 3
6 – 3 = 3
3 = 3