Construction Technology Solve Systems of Equations by Graphing

Construction Technology Solve Systems of Equations by Graphing 1

Bellwork • Think about your definition of the term intersection. • Write your definition on your notetaker. • Share with your partner.

Possible answers • Intersection – a place where 2 or more roads meet – geometric figures that have points in common – a set consisting of all those members that belong to two or more sets. • The intersection of {1, 3, 5} and {3, 4, 5, 6} is {3, 5}

Math Check 1. Graph the line y = 3 x -1 1. Graph 2 x + y = 5

Math Check Answer 1 1. Graph y = 3 x - 1 run = 1 rise = 3 y-intercept = -1

Math Check Answer 2 2. Solve 2 x + y = 5 for y y = -2 x + 5

Objectives 1. Define terminology 2. Explain the steps in solving a system of equations by graphing 3. Solve a real world auto problem by graphing systems of equations

Terminology • System of equations – consists of two or more equations that have the same variables where each equations represents a line.

Construction Problem Pleaserevise. com • Al has twice as many calls for roof repairs as Bob. The cost for each of Al’s repairs was $200 and the cost for each of Bob’s repairs was $100. The combined cost for all repairs was $1, 000 for Monday. How many of roof repairs did each of the foreman make?

Steps to solve a system of equations 1. Identify the important information 2. Define the 2 variables 3. Write 2 equations 4. Select a method to solve fotosearch. com

Identification Underline most important information PROPERTY OF AZ CTE CURRICULUM CONSORTIUM, 2013

Methods to Solve The problem has two variables and two equations. To 1. 2. 3. solve we can use: Graphing Substitution Elimination or Addition No matter which method you use, you will get the same answer! Always write your answer as an ordered pair or label each.

Steps in Graphing Method 1. Rewrite each equation in form (slope-intercept form) 2. Graph each line 3. Identify the point of intersection mediaweek. co. uk

e s a r h p a r a P n i s p e t s 3 e h t e z i r s. Summa d r o w n your ow . r e n t r a p ur o y h t i w hare S PROPERTY OF AZ CTE CURRICULUM CONSORTIUM, 2013

Graphing Method Step 2 (3, 1) Step 1 x = 3 and y = 1 Step 3

Graphing Method Example What is the point of intersection?

Graphing Method Example Point of Intersection What is the point of intersection? (5, 3)

Example • Think of two numbers who add together to equal 8 and when subtracted equal 2. • What are the two numbers? • Share with your partner.

Example Answer The numbers are 5 and 3. Let’s use this example to solve using the graphing method

Solve this system • Think of two numbers who add together to equal 8 and when subtracted equal 2. • Let x = the first number y = the second number

Solve for y • Solve each equation for y

Graphing Method 1. Slope-intercept form

Graph y=-x+8 y=x+2

Graph and Intersection (5, 3)

U-try Graph and state the point of intersection

U-try Answer Step 1 • Step 1 – rewrite as •

U-try Answer Step 2

U try Answer Step 3 (1, -1)

Let’s Solve • Al has twice as many calls for roof repairs as Bob. The cost for each of Al’s repairs was $200 and the cost for each of Bob’s repairs was $100. The combined cost for all repairs was $1, 000 for Monday. How many of roof repairs did each of the foreman make?

Identification Underline the important information PROPERTY OF AZ CTE CURRICULUM CONSORTIUM, 2013

Let’s Solve – Important Information • Al has twice as many calls for roof repairs as Bob. The cost for each of Al’s repairs was $200 and the cost for each of Bob’s repairs was $100. The combined cost for all repairs was $1, 000 for Monday. How many of roof repairs did each of the foreman make?

Let’s write the equations Let x = Al’s repairs Let y = Bob’s repairs x = 2 y 200 x + 100 y = 1000

Solve each equation for y

Graph What does the intersection mean?

What does the intersection mean? (4, 2) Remember x = number of Al’s repairs y = number of Bob’s repairs So (4, 2) means 4 Al repairs and 2 Bob repairs on Monday

U-try A piece of pvc pipe is 30 inches long is cut into two pieces with one part being four times the length of the other. How long is each piece? ewingirragtaiong. com

U-try Equations A piece of pvc pipe is 30 inches long is cut into two pieces with one part being four times the length of the other. How long is each piece? Ewingirragation. com

Larger piece Graph for U-try Smaller piece

Graph for U-try Intersection Larger piece (4”, 16”) Smaller piece Small piece is 4” and large piece is 16”

Think-Pair-Share What are some advantages and disadvantages of the graphing method to solve systems of equations? PROPERTY OF AZ CTE CURRICULUM CONSORTIUM, 2013

Benefits and Challenges • Benefits – Visual – Relatively easy to do – Requires little algebra • Challenges – Not very accurate – Hard to do if the numbers are large

12 Word Summary Closure 48 37 21 13 14 18 23 In 12 words or less, summarize the most important aspects from today's lesson.