Section 7 – 2 Solving Systems Using Substitution

Slides:

Advertisements

Similar presentations

REVIEW for TEST Parallel and Perpendicular Solving Systems of Equations.

Advertisements

Systems of Equations & Inequalities

7.2, 7.3 Solving by Substitution and Elimination

Systems. Day 1 Systems of Linear Equations System of Linear Equations: two or more linear equations together The solution of the system of equations.

Objectives: To solve systems of equations by graphing.

CHAPTER 2 Solving Equations and Inequalities Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 2.1Solving Equations: The Addition Principle.

Algebra II  To solve equations  To solve problems by writing equations.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Rewrite Equations and Formulas Lesson 3.8 OBJ: To recognize and solve literal equations; to rewrite equations and formulas.

Chapter 2 Sections 5-6 Problem Solving and Formulas.

Solving Equations with Grouping Symbols

1.3 Solving Linear Equations. Equation: a statement in which two expressions are equal Linear Equation- One variable equation that can be written as ax.

Solving systems of equations with 2 variables

Geometry Section 6.1 Ratios, Proportions, and the Geometric Mean.

Sullivan Algebra and Trigonometry: Section 1.2 Quadratic Equations Objectives of this Section Solve a Quadratic Equation by Factoring Know How to Complete.

EXAMPLE 2 Rewrite a formula with three variables SOLUTION Solve the formula for w. STEP 1 P = 2l + 2w P – 2l = 2w P – 2l 2 = w Write perimeter formula.

Ratio and Proportion 7-1.

Lesson 5.6-Number Problems Obj: To solve # word problems.

12/12/ : Using Formulas Expectation: You will be able to use the formulas for area and perimeter of a rectangle to calculate (with correct units)

Solving Linear Systems Algebraically with Substitution Section 3-2 Pages

DateLessonClassworkHomework M, 1/3/11Welcome Back! Happy New Year! Where were we? Review methods of solving systems (graphing, substitution) Begin elimination.

Day Problems Solve by graphing. Check your solution.

Warm-up Solve the first system of equations by the Substitution Method, then graphing.

Happy Tuesday  Ready for a great 4 day week. Warm – up #3.

Do Now 9/23/09 Take out HW from last night. - Textbook page 95, #1-13 all - Textbook page 95, #1-13 all Copy HW in planner. - Textbook page , #14-24.

Solve Linear Systems by Substitution January 28, 2014 Pages

Solve the following word problem. Manny is two years older Enrique. The sum of the their ages is 40. How old is Manny and Enrique? Let: m = Manny’s age.

Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 1 Equations and Inequalities.

Section 7 – 3 Solving Systems Using Elimination Objectives: To solve systems by adding or subtracting To multiply first when solving systems.

Y=3x+1 y 5x + 2 =13 Solution: (, ) Solve: Do you have an equation already solved for y or x?

ALGEBRA 1 Lesson 6-2 Warm-Up. ALGEBRA 1 “Solving Systems Using Substitution” (6-2) How do you use the substitution method to find a solution for a system.

$100 $400 $300$200$400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500 Graphing Systems of Equations Substitution.

Section Solve one of the equations for one of its variables. 2.Substitute the expression for #1 into the other equation and solve for the other.

Warm-up 1. Solve the following system of equations by graphing: 3x – y = -3 y – 3x = Determine the solution type from the following system of equations:

Lesson Days Equations and Problem Solving Pages

Algebra 2 Lesson 1-3 Examples (part 2). Solving Equations A solution to an equation is __________________________________________ __________________________________________.

Lesson 1-3 Solving Equations. Properties of Equality Reflexive Propertya = a Symmetric PropertyIf a = b, then b = a. Transitive PropertyIf a = b and b.

Systems of Equations & Inequalities

Sullivan Algebra and Trigonometry: Section 1.2 Quadratic Equations

Chapter 12 Section 1.

Rewrite a formula with three variables

3.2 Substitution & Elimination

Warm Up Solve each equation. 1. y – 4 = 3x – 8, for x

3.2 Substitution & Elimination

Systems of Equations – Solving by Substitution

CHAPTER 3 SECTION 7.

1-5 Equations Goals: Solve equations with one variable

Friday Warmup Homework Check: Document Camera.

Solving Systems Using Substitution

Solving Systems Using Substitution

Solving Systems using Substitution

Solve a system of linear equation in two variables

Use the substitution method to find all solutions of the system of equations {image} Choose the answer from the following: (10, 2) (2, 10) (5, - 2) ( -

Ratio Ratio – a comparison of numbers A ratio can be written 3 ways:

In all things of nature there is something of the marvelous.

King of the Mountain.

8.4 Using Systems Objective:

Page 6 Original Expression: Step 1: Step 2: Step 3:

Problem Solving and Using Formulas

Algebra 2 Ch.3 Notes Page 15 P Solving Systems Algebraically.

Warm Up #30: Solve by substitution

Rewrite Equations and Formulas

Solving Linear Systems by Substitution

one of the equations for one of its variables Example: -x + y = 1

8.3 The Addition Method Also referred to as Elimination Method.

Section 1.5 Solving Equations.

Goal: The learner will find area and perimeter.

Chapter 2: Solving One-step Equations and Inequalities

Algebra 1 Section 7.2.

Presentation transcript:

Section 7 – 2 Solving Systems Using Substitution Objective: To solve systems using substitution

Investigation: Estimating Solutions

Substitution Method: A method for solving a system of equations in which one variable is replaced with an equivalent expression containing the other variable. Example: y = 3x + 2 4x + y = 9

Example 1 Using Substitution A) Solve using substitution. y = -4x + 8 y = x + 7

B) Solve using substitution. y = 2x + 2 y = -3x + 4

C) Solve using substitution. y = 3x – 1 y = -2x + 4

D) Solve using substitution. y = 4x + 7 y = -3x

1) y = x + 1 2) y = 2x + 5 y = 2x – 1 y = 6x + 1 3) 2y = x + 3 4) x – y = 1 x = y x = 1/2y + 2

Homework: Textbook Page 350; #5 – 10

Objective: To solve systems using substitution Section 7 – 2 Continued… Objective: To solve systems using substitution

Example 2 A) Solve using substitution. 2y = x + 3 x = y

B) Solve using substitution. x – y = 1 x = 1/2y + 2

C) Solve using substitution. y = 2x 7x – y = 15

D) Solve using substitution. y = -3x + 4 2x – y = 6

SPECIAL CASES Solve using substitution. 1) y = 3x – 6 2) x = y + 4 -3x + y = -6 y = x + 4

Classwork/Homework 7 – 2 Ditto: #1, 4, 7, 8, 9, 10

Answers to 7 – 1 Assignment 1) (1, 1) 4) (-3, 2) 7) (5, -2) 8) Infinitely Many 9) (100, 50) 10) No Solution

Section 7 – 2 Continued… (Day 3) Objective: To solve systems using substitution

Example 3 Using Substitution & the Distributive Property A) Solve using substitution. 6x + 6y = -6 5x + y = -13

B) Solve using substitution. 3x + y = 4 2x – y = 6

C) Solve using substitution. -5x + y = - 2 -3x + 6y = -12

D) Solve using substitution. -2x + y = -1 4x + 2y = 12

E) Solve using substitution. 3y + 2x = 4 -6x + y = -7

F) Solve using substitution. 6y + 8x = 28 3 = 2x – y

Section 7 – 2 Continued… (Day 4) Objective: To solve systems using substitution

Example 4 Real-World Problem Solving A) Your school committee is planning an after-school trip to take 193 students to a competition at another school. There are eight drivers available and two types of vehicles, school buses and minivans. The school buses seat 51 people each, and the minivans seat 8 people each. How many buses and minivans will be needed?

B). A youth group with 26 members is going to the beach B) A youth group with 26 members is going to the beach. There will also be five chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed?

C). A rectangle is 4 times longer than it is wide C) A rectangle is 4 times longer than it is wide. The perimeter of the rectangle is 30 cm. Find the dimensions of the rectangle.

D). The length of a rectangle is 5 cm more than twice the width D) The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.