10-4 Solving Systems by Addition To solve a system you can use , , or method. How do you use the addition method? 1. the.

Slides:

Advertisements

Similar presentations

Distance-Rate-Time Applications Example 1: Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home.

Advertisements

Solving Rational Equations and Inequalities

EXAMPLE 5 Write and solve an equation

Over Lesson 6–3. Splash Screen Solving Systems with Elimination Using Multiplication Lesson 6-4.

Name:__________ warm-up 6-4 Use elimination to solve the system of equations. 5x + y = 9 3x – y = 7 Use elimination to solve the system of equations. 2x.

Wind and Current Word Problems

Algebra 7.3 Solving Linear Systems by Linear Combinations.

Solving Systems of Equations

Part 2.  Review…  Solve the following system by elimination:  x + 2y = 1 5x – 4y = -23  (2)x + (2)2y = 2(1)  2x + 4y = 2 5x – 4y = -23  7x = -21.

Solving a System of Equations using Multiplication

Warm Up What is the LCM of 3x and –4x ? What is the LCM of 5y and 2y ?

When solving an application that involves two unknowns, sometimes it is convenient to use a system of linear equations in two variables.

Solving Linear Systems by Linear Combinations

Math 140 Quiz 5 - Summer 2006 Solution Review (Small white numbers next to problem number represent its difficulty as per cent getting it wrong.)

Applications for Systems of Equations Algebra I. Example #1  Flying to Ankara with a tailwind a plane averaged 368 mph. On the return trip the plane.

Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to.

Can I use elimination to solve this system of equations? 2x + y = 23 3x + 2y = 37.

Using Linear Systems to Solve Application Problems:  1. Define the variables. There will be two unknown values that you are trying to find. Give each.

LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems.

When a computer solves matrix equations, taking the inverse of the matrix is problematic. MATLAB employs other means to do the arithmetic. Today we are.

Solve by using the ELIMINATION method The goal is to eliminate one of the variables by performing multiplication on the equations. Multiplication is not.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

A set of linear equations involving the two variables A solution is the intersection of the two lines. One of three things can happen: 11.1 Systems of.

ACTIVITY 20: Systems of Linear Equations (Section 6.2, pp ) in Two Variables.

CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.

Preview Warm Up California Standards Lesson Presentation.

Solving Linear Systems Using Linear Combinations There are two methods of solving a system of equations algebraically: Elimination (Linear Combinations)

Section 2.1 Systems of Equations (no calculator).

Rational Equations Technical Definition: An equation that contains a rational expression Practical Definition: An equation that has a variable in a denominator.

Solving Rational Equations & Inequalities

KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.

Warm Up Simplify each expression. 1. 3(10a + 4) – (20 – t) + 8t 3. (8m + 2n) – (5m + 3n) 30a t 3m – n 4. y – 2x = 4 x + y = 7 Solve by.

Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.

£ ≈ ∑ Chapter 9: Test Your Proficiency Directions: Select a section to work on. Work out each problem on a piece of paper. Click to check your answer.

4-3 Solving Multiplication Equations Standard : PFA Indicator: P9 (same as 4-2)

6-4: Elimination using Multiplication

8-5 Motion d=rt 9P9: Interpret systems. Types of motion Problems T1) Distance covered is equal (d = d) T2) Distance covered is equal + wind or current.

7.2 Two-Variable Linear Systems Elimination method.

Motion Problems(wind/water) Review Homework 191 # # # 46.

Systems of Equations & Inequalities Mrs. Daniel Algebra 1.

D = r . t r = Solve for rate Motion Word Problems - continued

6-5 Applying Systems 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically.

Chapter Seven 7.2 – Systems of Linear Equations in Two Variables.

Solving Systems of Equations by Elimination (6-3, 6-4) Objective: Solve systems of equations by using elimination with addition, subtraction, and multiplication.

Solving Real World Linear Systems of Equations with Two Variables Objective: Review writing and solving linear systems of equations with two variables.

PreCalculus 7-R Unit 7 System of Equations and Matrices Review Problems.

Solving Application Problems Using System of Equations Section 4.3.

Elimination Using Multiplication

Solving Linear Systems

1. Solve the linear system using substitution.

Summary of Methods Substitution: Requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the.

Solving Systems of Linear Equations

Section 8.1 Solving Systems of Linear Equations by Graphing.

Systems of Linear Equations in Two Variables

isolate inverse opposite constants coefficients reciprocal subtraction

REVIEW: Solving Linear Systems by Elimination

Solve Systems of Equations by Elimination

Solving Equations Containing

Elimination Using Multiplication

Warm Up Lesson Presentation Lesson Quiz

Welcome to Interactive Chalkboard

Notes Solving a System by Elimination

Notes Solving a System by Elimination

5-A9 Wind and Current Word Problems

College Algebra Chapter 5 Systems of Equations and Inequalities

Expressions and Equations Notes Part 11

Presentation transcript:

10-4 Solving Systems by Addition To solve a system you can use ________, __________, or ______ method. How do you use the addition method? 1. ____ the 2 equations together to _____ a ________. 2. Find the _____ of the _______ left. 3. _________ that _____ into one of the ________ to find the ____________.

1. Going with the wind, a blimp flies 360 miles to an air show. The trip takes 4 hours. The return trip, flying against the wind, takes 9 hours. How fast is the blimp flying in still air? What is the speed of the wind? Let b=speed of blimp in still air Let w=speed of the air d=rt or d/t=rw’s are opposites

2. Solve this system. 2x - 5y = 18 4x - 5y = -4 { They do not have opposite variables, but if you take the opposite of one equation, the y’s would become opposites. -() Solution is ( )

3. At the 1987 annual meeting of the NCTM, the system below was found on a menu card at a restaurant in California. How much did each item in column A and column B cost? Multiple Choice 2 or more entrees Choose 1 from column A and 1 from column B - $5.49 Choose 1 from column A and 2 from column B - $6.99 A B ·Chicken Dijon · Fried Chicken ·Top Sirloin Steak (2 pieces) ·Steak Dijon ·Battered Cod ·Fried Chicken ·Shrimp ·Chicken Strips A + B = $5.49 A + 2B = $6.99

Item A costs and item B costs.