1. MS Algebra A-F-IF-7 – Ch. 7.2 Solve Linear Systems by Substitution
ALGEBRA SUPPORT (Homework)
Solve Linear Systems by Substitution

2. SUPPORT Learning Target
Title: 7.2 Solve Linear Systems by substitution
Date:
SUPPORT Learning Target
By the end of the period, I will solve linear systems by substitution.
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 7.2 Pg ) Section ______
TxtBk.Prob.#3,15,17,27,29,32,33 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. 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)

5. Solving Systems by Substitution
Notes:
Step 1: Solve one of the equations for one of its variables that has a coefficient of 1 or -1. (Here we choose y.)
Step 2: Substitute the expression from Step 1 into the other equation and solve for the other variable. (Here the “other” variable is x).
Here we choose Equation 1 where y = (2x - 1)
Here we substitute (2x - 1) for y in Equation 2.
Equation 1: y = 2x - 1
Equation 2: 2x + y = 3
Equation 2: 2x + (2x - 1) = 3
2x + 2x -1 = 3
4x – 1 = 3
4x = 4
x = 1
Step 3: Substitute the expression from Step 2 back into Equation 1 and solve for the first variable. (Here the 1st variable is y.)
y = 2x – 1
y = 2(1) – 1
y = 2 – 1 = 1
Step 4: Check your solution
Solution:
(1, 1)
Equation 1: 1 = 2(1)- 1
Equation 2: 2(1)+(1) = 3

6. x = 17 – 4y y = x - 2 Solve the linear system. HW # 3 Equation 1
Solve for best variable & Use the substitution method
Equation 1
STEP 1 Choose a variable
and solve.
STEP 2 Substitute in Eq. 2
AND Solve for 2nd variable.
STEP 3 Substitute in Eq. 1
AND Solve for 1st Variable.
STEP 4 Check Solution
Equation 2
x = 17 – 4y
y = x - 2

7. 5x + 2y = 9 x + y = -3 Solve the linear system. HW # 15 Equation 1
Solve for best variable & Use the substitution method
Equation 1
STEP 1 Choose a variable
and solve.
STEP 2 Substitute in Eq. 2
AND Solve for 2nd variable.
STEP 3 Substitute in Eq. 1
AND Solve for 1st Variable.
STEP 4 Check Solution
Equation 2
5x + 2y = 9
x + y = -3

8. 5x + 4y = 32 9x – y = 33 Solve the linear system. HW # 17 Equation 1
Solve for best variable & Use the substitution method
Equation 1
STEP 1 Choose a variable
and solve.
STEP 2 Substitute in Eq. 2
AND Solve for 2nd variable.
STEP 3 Substitute in Eq. 1
AND Solve for 1st Variable.
STEP 4 Check Solution
Equation 2
5x + 4y = 32
9x – y = 33

9. Storm Check (Think, Write, Discuss, Report)
Explain in your own words the four steps of solving systems of equations by substitution?
The four steps of solving systems of equations by substitution are:
1) _________________________________________
2) _________________________________________
3) _________________________________________
4) _________________________________________

10. Write & Solve a Linear System That Models the Situation
HW # 27
For use with pages xxx–xxx
The perimeter of a rectangle is 32 inches. The length is 3 times the width.

11. Write & Solve a Linear System That Models the Situation
HW # 29
For use with pages xxx–xxx
During a football game, students sell drinks and popcorn. They charge $2.50 for a bag of popcorn and $2 for a drink. The students collect $336 in sales. They sell twice as many bags of popcorn as drinks. How many bags of popcorn do they sell?
48 bags
52 bags
96 bags
104 bags

12. Write & Solve a Linear System That Models the Situation HW # 32 A
For use with pages xxx–xxx
For a floral arrangement class, every student has to create an arrangement of daisies and irises that has a total of 15 flowers. Students have to pay for the daisies and irises that they use in their arrangements. Each daisy costs $1.15, and each iris costs $0.75. Suppose a student spends $12.85 on the daisies and irises. Write and solve a linear system to find the number of daises and the number of irises the student uses.

13. Make a Table HW # 32 B 1 2 3 4 5 For use with pages xxx–xxx
For a floral arrangement class, every student has to create an arrangement of daisies and irises that has a total of 15 flowers. Students have to pay for the daisies and irises that they use in their arrangements. Each daisy costs $1.15, and each iris costs $0.75. Check your answer from Part A by making a table that shows the number of irises in the arrangement and the total cost of the arrangement when the number of daisies purchased is 0, 1, 2, 3, 4, or 5.
# Daisies
# Daisies • $1.15
# Irises
# Irises • $0.75
Total Cost 1 2 3 4 5

14. Write & Solve a Linear System That Models the Situation HW # 33
For use with pages xxx–xxx
A gazelle can run 73 feet per second for several minutes. A cheetah can run 88 feet per second, but it can sustain this speed for only 20 seconds. A gazelle is 350 feet from a cheetah when both animals start running. Can the gazelle stay ahead of the cheetah? Explain.

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

16. 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

17. Storm Check (Think, Write, Discuss, Report)
To verify your solution to a system of linear equations, what do you have to do?
To verify my solution to a system of linear
equations, I have to _________________________
___________________________________________
___________________________________________.