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

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.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 7.2 Pg. 386-388 3) 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

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)

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

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

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

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

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) _________________________________________

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.

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

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.

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

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.

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

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

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 _________________________ ___________________________________________ ___________________________________________.