Applications of Systems of Linear Equations

Slides:

Advertisements

Similar presentations

8.6 Coin and Ticket Problems CA Standard 9.0CA Standard 9.0 Two Key TermsTwo Key Terms.

Advertisements

Systems of Linear Equations Vocabulary. This is a System of Linear Equations.

Distribution in Percentage Equations and Word Problems

A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 5.1 – Systems of Linear Equations.

Solve Systems of Linear Equations in Three Variables. Section 3.4.

Section 7.5: System of Linear Equations & Problem Solving 3 examples of how to set-up and solve word problems using systems of equations.

Monday, March 23 Today's Objectives

Systems of Two Equations in Two Unknowns In order to explain what we mean by a system of equations, we consider the following: Problem. A pile of 9 coins.

3.1 Solve Linear Systems by Graphing. Vocabulary System of two linear equations: consists of two equations that can be written in standard or slope intercept.

Slide Systems of Linear Equations A system of linear equations consists two or more linear equations.

Check it out! 2.2.2: Solving Systems of Linear Equations 1.

Linear Equations, Inequalities, and Absolute Value

Table of Contents The goal in solving a linear system of equations is to find the values of the variables that satisfy all of the equations in the system.

Section 4.2 Solving Linear Inequalities Using the Multiplication-Division Principle.

Solving Systems of Equations using Substitution

Complete pg in Student Journal

Warm-Up 1. Use the graph to solve the linear system. SHOW THE WORK for checking your solution. 3x – y = 5 -x + 3y = 1 (2,1)

Class 5: Question 1 Which of the following systems of equations can be represented by the graph below?

10.8 Mixture Problems Goal: To solve problems involving the mixture of substances.

Solving Systems of Equations Classic Applications (Mixture & Money)

Objective : Solving systems of linear equations by graphing System of linear equation two or more linear equations How do I solve linear systems of equations?

Let’s Learn About Money!

Ch4: Systems of Linear Equations y x y x y x y = ½ x –3 Consistent y = (-2/3)x + 2 Independent Equations One Solution (x, y) y = ½ x - 3 y = ½ x + 2 Inconsistent.

Warm-Up: Put the following equations into y= mx + b form: a) 2y + 14x = 6b) -3y – 4x – 15 = 0.

Solution problems. PercentAmountmixture 60%.6 x.6x 20%.25 1 End product-50%.5X+5.5(x+5) 1. How liters of a 60% solution must be added to 5 gallons of.

Section 3.2 Connections to Algebra.  In algebra, you learned a system of two linear equations in x and y can have exactly one solution, no solutions,

Solve the system of equations using the graphing method. y = x – 5 x + 2y = − 4 Find the x and y.

EXAMPLE 4 Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects.

Linear Systems of Equations Section 3.1. What is a “system” of equations?

1 Beginning & Intermediate Algebra – Math 103 Math, Statistics & Physics.

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 1 Applications and.

3.1 Solving Systems Using Tables and Graphs When you have two or more related unknowns, you may be able to represent their relationship with a system of.

10-8 Mixture Problems Standard 15.0: Apply algebraic techniques to percent mixture problems. Standard 15.0: Apply algebraic techniques to percent mixture.

Lesson 2-6 Warm-Up.

Solving Linear Systems Algebraically Section 3-2 Solving Linear Systems Algebraically.

Algebra 7.2 Solving Systems Using Substitution. You have already learned that the solution is the point of intersection of the two graphed lines. Solution.

Warm–up #3 1. Find two consecutive integers whose product is If $7000 is invested at 7% per year, how much additional money needs to be invested.

Betty Bob has six more nickels than dimes. The total amount of money she has is $3.30. How many of each coins does she have? Warm Up.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

Applications of Systems of Equations. Three Steps to solving applications  Step 1: NAME YOUR VARIABLES!! What are you looking for and what are you going.

Algebra 1 Foundations, pg 382  Students will be able to solve systems of equations by graphing. You can make a table, use the formula r * t = d, or write.

6-4: Applications of Linear Systems Algebra 1. Solving a System Graphing: When you want a __________ display of when you want to estimate the solution.

APPLICATIONS OF LINEAR SYSTEMS: PERCENT AND MIXTURE PROBLEMS.

Ch. 7 – Matrices and Systems of Equations Elimination.

You Will Be Able To: Write and Solve Systems Word Problems.

A.2(I) write systems of two linear equations given a table of values, a graph, and a verbal description Performance: write given a table of values, a graph,

Algebra 1 Section 7.1 Solve systems of linear equations by graphing Recall: linear equation in 2 variables ax + by = c The solution to a system of equations.

Algebra 1 Section 4.2 Graph linear equation using tables The solution to an equation in two variables is a set of ordered pairs that makes it true. Is.

Algebra 1 Chapter 1 review. Algebra I – Chapter 1 Review.

2( ) 8x + 14y = 4 -12x – 14y = x = x = 4 8x + 14y = 4 8(4) + 14y = y = y = -28 ___ ___ y = -2 The solution is (4, -2)

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

10.8 Mixture Problems Goal: To solve problems involving the mixture of substances.

Warm-Up Graph Solve for y: Graph line #2.

Do Now Solve the following systems by what is stated: Substitution

MATH 1311 Section 3.5.

Equations and Problem Solving

Coin Combinations Systems of Equations

MATH 1311 Section 3.5.

Solving Systems of Linear and Quadratic Equations

Graphing systems of linear equations and inequalities

Section 7.1 “Solve Linear Systems by Graphing”

Solving Systems of Linear and Quadratic Equations

Today we will Graph Linear Equations

Section Quick Graphs of Linear Equations

Where do these graphs intersect

Linear and Nonlinear Systems of Equations

Linear and Nonlinear Systems of Equations

Section 8.4 Chapter 8 Systems of Linear Equations in Two Variables

Chapter 3 Section 6 Applications.

Presentation transcript:

Applications of Systems of Linear Equations i.e. Word Problems!!!

Piggy Bank A child has 25 coins in a piggy bank consisting of dimes and quarters. The total value of the coins is $3.70. Find the number of dimes and the number of quarters.

Piggy Bank We have two unknowns in this problem, Let d = Let q = We have two totals we are concerned with, The total number of ____________ The total amount of ____________

Piggy Bank How can we verbally represent the total number of coins? How can we algebraically represent the total number of coins?

Piggy Bank How can we verbally represent the total amount of money in the piggy bank? How can we algebraically represent the total amount of money in the piggy bank?

Piggy Bank We have two linear equations – what should we do??

The Chemist You are in Chem. lab and in order to pass your lab you need to make 3 gallons of a solution that is 12% acid. To make the required mixture you need to mix two solutions. One solution is 8% acid and another is 18% acid. How many gallons of each acid should be mixed to produce 30 gallons of a solution that is 12% acid?

The Chemist We have two unknowns in this problem, Let x = Let y = We have two totals we are concerned with, The total volume of ____________

The Chemist How can we verbally represent the total volume of solution? How can we algebraically represent the total volume of solution?

The Chemist How can we verbally represent the total volume of acid? How can we algebraically represent the total volume of acid?

The Chemist Again we have two linear equations – what should we do???

The Entrepreneur Lavely Inc. has daily fixed costs from salaries, rent, and other operations of $600. Each widget Lavely Inc makes costs $25 and sells for $45. a.) Determine the cost C of producing x widgets per day.

The Entrepreneur b.) Determine the revenue R of selling x widgets per day.

The Entrepreneur c.) Graph the cost and revenue functions – what does the intersection represent?