Get variables on the same side & line up x, y, and z.

Slides:



Advertisements
Similar presentations
Warm Up.
Advertisements

Percent Word Problems.
Jeopardy AnimalsSportsFoodSchool Toys Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy.
HW: Page 11 #7-21 ANSWERS. 1-3 Solving Addition and Subtraction Equations Pre-Algebra 1-3 Solving Addition and Subtraction Equations Pre-Algebra Warm.
Quiz Evaluate each expression for the given values of the variables. 1. 6x + 9 for x = x + 3y for x = 4, y = 2 3. If n is the amount of money in.
Solving Multi-Step Equations
Hosted By Mrs. Shook Pattern or Total Find the missing pattern Fine the total of the pattern
5 Minute Check. Solve and show work on the back on your homework. 3. d + 4 = 36.
Lesson #13- Translating Words into Math
3.5 Word Problems. The sum of two numbers is 97. The second number is 11 less than the first. Find the numbers. Let x = the first number Let y = the second.
Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains.
Unit 6 Baseball Chapter 8: Systems Created © 2007 by Alice Keeler
HW # 76 - p. 142 & 143 # 1-40 even SHOW YOUR WORK! Warm up Week 23, Day One Compare. Use –3 – – –8 –7 Solve y = 166. m.
Monday’s Warm Up Helen is now 20 years old and Arlene is 10 years old. How many years ago was Helen three times as old as Arlene was then? 5 years ago,
Trapezoid Write a decimal that could make the sentence correct. 1. ? 0.3 < > 0.50.
Solving Algebraic Equations. How do I Solve Algebraic Equations? 1.What ever you add, subtract, multiply or divide to one side of the equation, you have.
x x x < 1or x < 3 x < 3.
Warm Up. Lesson 63: Solving Systems of Linear Equations by Elimination Expressions and Equations.
Equations and Problem Solving
How do you use an equation to show the relationship between two variables? j = 10s.
Lesson 1.1 Using Variables. 1.1 – Using Variables Goals / “I can…” Model relationships with variables Model relationships with equations.
CHAPTER 2: Linear Equations, Inequalities and Applications LESSON 2.2 FORMULAS OBJECTIVES:
Unit conversion The formula for density d is
Section 2.1 Systems of Equations (no calculator).
How do we translate between the various representations of functions?
(For help, go to Lesson 1-1.) ALGEBRA 1 LESSON 2-7 Write a variable expression for each situation. 1.value in cents of q quarters 2.twice the length 3.number.
1.3 Algebraic Expressions Which algebraic expression models the word phrase seven fewer than a number t ? A. t + 7C. t – 7 B. -7tD. 7 – t The correct answer.
DO NOW Nov , Monday, November 9, 2015 LG: Understand Positive and Negative Numbers HW: PB pgs #1-9 DO NOW: What are the steps of.
Get radical alone. 5 Tues 1/12 Lesson 6 – 5 Learning Objective: To solve radical equations Hw: Lesson 6 – 5 WS 2.
Mon 1/11 Lesson 6 – 5 Learning Objective: To solve square root equations Hw: Lesson 6 – 5 WS 1.
Wednesday, November 10 Objective: Students will identify solutions of inequalities and write inequalities. Today’s Agenda: 1.Practice 3-3 is due 2.Fill.
8 th Grade Ciphering. Sample 1 st Interval2 nd Interval3 rd Interval.
Solving Problems using Tables and Graphs Chapter 4.
Warm up 1. Convert 5,400 inches to miles. (1 mi = 5280 ft) 2. Convert 16 weeks to seconds 3. Convert 36 cm per second to miles per hour. (1 in = 2.54 cm)
November 12 th, 2015 Ms.Naumann Algebra. Warm Up Think back to yesterdays situation…The Marshall High School Athletic Association sells tickets for the.
1.11 Applications with systems I can… write and solve my own systems of linear equations.
Fri 10/23 Lesson Rev Learning Objective: To remember everything learned in Chapter 3! Hw: Chapter 3 Review WS 1.
LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.
Objectives: 1.Be able to write equations of application problems. 2.Be able to solve applications using substitution or elimination. Critical Vocabulary:
Warm up miles 9,676,800 seconds mph
Bellwork 1. A salesman's salary is $18,500 per year. In addition, the salesman earns 5% commission on the year's sales. Last year the salesman earned $25,400.
Write an equation for each of the following.
Solving One-Step Equations
Opening Routine The total ticket sales for a high school basketball game were $2,260. The ticket price for students was $2.25 less than the adult ticket.
Solving Systems Using Elimination
Warm Up Determine if the given numbers are solutions to the given equations. 1. x = 2 for 4x = 9 2. x = 5 for 8x + 2 = x = 4 for 3(x – 2) = 10 no.
Notes Over 4.2 The Multiplication Property of Equality
Consecutive Number Equations
Warm – up Toya is training for a triathlon and wants to bike and run on the same day. She has less than 3 hours to spend on her workouts. What inequality.
Warm up miles 9,676,800 seconds mph
Equations and Problem Solving
Solving Multi-Step Equations
Warm up Interpret the following: “The quotient of a number cubed and twelve plus twice a different number” Solve for “m”: 22 = 5m + 7.
Unit 6 Baseball Chapter 8: Systems
Solving Systems Using Elimination
Bellwork Solve the following by: y = 2x y = x ) Graphing
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Math Review Activity! Combining Like terms, solving equations, Solving Inequalities, Problem Solving Strategies Created by Educational Technology Network.
Solving Word Problems Using Systems
Warm up 15.8 miles 31,536,000 seconds mph
Coordinate Algebra Day 11
To solve an equation means to find a solution to the equation
Expressions and Properties
Warm Up Determine if the given numbers are solutions to the given equations. 1. x = 2 for 4x = 9 2. x = 5 for 8x + 2 = x = 4 for 3(x – 2) = 10 no.
Solving Equations with Variables on Both Sides
Warm up Solve the given system by substitution: 2x – y = 7
6.3 Percent Equation Objective: Today we want to be able to identify the percent equation. We will also learn how to use the equation to solve percent.
Do Now Solve. 1. x – 17 = y + 11 = = x = -108
6-3 Solving Systems Using Elimination (Combination)
Using Variables ALGEBRA 1 LESSON 1-1
Presentation transcript:

Get variables on the same side & line up x, y, and z

-x + 2y – z = 5 x – 3y – 2z = -7 -y – 3z = -2 2x + 4y + 3z =6 -2x + 6y + 4z = 14 10y + 7z = 20 (-1)( ) (-1) (-2)( ) (-2)

-10y – 30z = y + 7z = z = 0 z = 0 (-1, 2, 0) 10y + 7(0) = 20 10y = 20 y = 2 x – 2(0) = 3(2) – 7 x – 0 = 6 – 7 x = -1 (10)( ) (10)

Thurs 10/22 Lesson 3 – 5 Learning Objective: To solve word problems with systems Hw: Lesson 3 – 5 Word Problems WS

Algebra II

 To solve word problems using systems of equations

1. Find the value of two numbers if their sum is 19 and their difference is 3. x + y = 19 x – y = 3 2x = 22 x = y = 19 y = 8 {8, 11}

2. On the first day of choir ticket sales, 12 adults and 1 student ticket sold for a total of $171. Choir took in $138 on the second day be selling 6 adult tickets and 4 student tickets. Find the price of an adult and a student ticket. 12x + y = 171 6x + 4y = 138 (-4) -48x - 4y =-684 6x + 4y = x = -546 x = 13 12(13) + y = y = 171 y = 15 $13 for adult tix $15 for student tix

3. Jacob sold 14 banana pies and 13 strawberry pies for a total of $241. Kim sold 2 banana pies and 6 strawberry pies for a total of $80. What is the cost of each pie? 14x + 13y = 241 2x + 6y = 80 (-7) 14x + 13y = x -42y = y = -319 y = 11 2x + 6(11) = 80 2x + 66 = 80 2x = 14 x = 7 $7 for banana pie $11 for strawberry

4. The sum of three numbers is 6. The third number is the sum of the first and second number. The first number is one more than the third number. Find the numbers. x = 1 st #y = 2 nd #z = 3 rd # x + y + z = 6 z = x + y x = z + 1 x + y + z = 6 x + y – z = 0 x - z = 1

4. x – 3 = 1 x = 4 x + y + z = 6 x + y – z = 0 x - z = 1 (-1) -x - y - z = -6 x + y – z = 0 -2z = -6 z = y + 3 = y = 6 y = -1 {4, -1, 3}

5. Anna is training for a triathlon. In her training routine each week, she runs 7 times as far as she swims and she bikes 3 times as far as she runs. One week, she trained a total of 232 miles. How far did she run that week? x = swimy = runz = bike x + y + z = 232 y = 7x z = 3y x + y + z = x + y = 0 -3y + z = 0

5. -7x + y = 0 x + 4y = 232 x + y + z = x + y = 0 -3y + z = 0 (-1) x + y + z = 232 3y – z = 0 x + 4y = 232 (-4) 28x -4 y = 0 x + 4y = x = 232 x = 8

5. y=7(8) y = 56 z = 3(56) z = 168 Swim 8 miles Run 56 miles Bike 168 miles

6. Sports Chalet sold 10 gloves, 3 bats, and 2 bases for $99 on Monday. On Tuesday, it sold 4 gloves, 8 bats, and 2 bases for $78. On Wednesday, it sold 2 gloves, 3 bats, and 1 base for $ What are the prices of each item? x = glovey = batz = base 10x + 3y + 2z = 99 4x + 8y + 2z = 78 2x + 3y + z = 33.60

6. 10x + 3y + 2z = 99 -4x – 6y – 2z = x – 3y = x + 3y + 2z = 99 4x + 8y + 2z = 78 2x + 3y + z = (-1) 10x + 3y + 2z = 99 -4x – 8y – 2z = -78 6x – 5y = 21 (-2)

6. 6x – 5y = 21 6x – 3y = 31.8 (-1) Glove $8 Bat $5.40 Base $ x + 5y = -21 6x – 3y = y = 10.8 y = 5.4 6x – 3(5.4) = x – 16.2 = x = 48 x = 8 4(8) + 8(5.4) + 2z = z = z = 78z = 1.4

7. The sum of three numbers is -4, The second number decreased by the third number is equal to the first. The sum of the first and second number is -6. What are the numbers? x = 1 st #y = 2 nd #z = 3 rd # x + y + z = -4 y – z = x x + y = -6 x + y + z = -4 -x + y – z = 0 x + y = -6

7. x + (-2) = -6 x = -4 x + y + z = -4 -x + y – z = 0 x + y = -6 x + y + z = -4 -x + y – z = 0 2y = -4 y = (-2) + z = z = -4 z = 2 {-4, -2, 2}

8. The difference of two number is 2. Their sum if 20. What are the numbers? x + y = 20 x – y = 2 2x = 22 x = y = 20 y = 9 {9, 11}

 LAHS scored 37 points in a football game. Six points are award for each touchdown. After each touchdown, the team can earn one point for the extra kick, or two points for a 2-point conversion. The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were made?