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

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.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 7.1 Pg. 378-381 3) 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

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

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

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

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

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)

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

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.

-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

-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 -1 + 4 = 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

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 ____________ ___________________________________________ __________________________________________.

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 = -7 Eq. 2: x + 4y = -8 STEP 1 Graph both equations STEP 2 Find intersection. STEP 3 Check solution Eq. 1: -x + y = -7 Eq. 2: x + 4y = -8

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 = -7 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 = -7 Eq. 2: x + 4y = -8 -(4) + (-3) = -7 -4 – 3 = -7 -7 = -7 4 + 4(-3) = -8 4 – 12 = -8 -8 = -8

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 = 0 Eq. 2: 5x + y = 10 STEP 1 Graph both equations STEP 2 Find intersection. STEP 3 Check solution Eq. 1: -5x + y = 0 Eq. 2: 5x + y = 10

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 = 0 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 = 0 Eq. 2: 5x + y = 10 -5(1) + (5) = 0 -5 + 5 = 0 0 = 0 5(1) + (5) = 10 5 + 5 = 10 10 = 10

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 ______________ ___________________________________________.

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

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

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 = 25 15x + 30y = 450 (20) + (5) = 25 15(20) + 30(5) = 450 25 = 25 300 + 150 = 450

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

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

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 = 18 15x + 30y = 390 (10) + (8) = 18 15(10) + 30(8) = 390 18 = 18 150 + 240 = 390

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

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 7.1 Pg. 378-381 3) 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

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.

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 = 5 Eq. 2: 3x + y = 3 STEP 1 Graph both equations STEP 2 Find intersection. STEP 3 Check solution Eq. 1: x – y = 5 Eq. 2: 3x + y = 3

-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 = 5 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 = 5 Eq. 2: 3x + y = 3 (2) - (-3) = 5 2 + 3 = 5 5 = 5 (2, -3) 3(2) + (-3) = 3 6 – 3 = 3 3 = 3