Lesson 5.4 The 3 kinds of systems

Slides:

Advertisements

Similar presentations

Standard 9 Solve a system of two linear equations.

Advertisements

SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.

Solve Systems of Equations & Graph Inequalities

7.1 Systems of Linear Equations: Two Equations Containing Two Variables.

Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A-REI.6; A-REI.7.

Solving System of Equations Using Graphing

7.1 Graphing Linear Systems

Math 71A 3.1 – Systems of Linear Equations in Two Variables 1.

ALGEBRA II SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS.

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

Complete the Literature Analysis from Monday. Use the resources on the internet and each other to help you relearn the concept. Use whiteboards. Use laptops.

Solving Systems of Linear Equations Tutorial 14a.

Do Now - Review Find the solution to the system of equations: x – y = 3 x + y = 5.

Lesson 7.5 Objective: To identify three types of linear systems The 3 kinds of systems 1)Regular system. When the two lines intersect once. One solution.

Objective I will identify the number of solutions a linear system has using one of the three methods used for solving linear systems.

Solving Systems of Linear Equations in Two Variables

Warm Up 12/5 1) Is (-2, 3) a solution? 3x + y = -3 3x + y = -3 2x – 4y = 6 2x – 4y = 6 2) Find the solution by graphing y = -4 + x x + y = 6 3) Solve:

Solving Systems Using Elimination

Math /4.2/4.3 – Solving Systems of Linear Equations 1.

Monday, March 23 Solve system of linear equations by graphing. Check consistency and dependency of system of equations by graphing.

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,

Solving System of Equations that have 0, 1, and Infinite Solutions

Ch 7: System of Equations E) Parallel & Same Lines Objective: To identify the number of solutions of a system of linear equations.

System of Equations Using Elimination. A System of Equations: Consists of two linear equations We want to find out information about the two lines: –T–The.

Section 4.1 Systems of Linear Equations in Two Variables.

Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:

Solving a System of Equations in Two Variables By Graphing Chapter 8.1.

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.

Types of Systems. Inconsistent of consistent? Example 1: 3x – y = 2 6x – 2y = 3 Example 2: x + y = -2 x -2y = 7.

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.

Solving Systems By Graphing. Warm – Up! 1. What are the 2 forms that equations can be in? 2. Graph the following two lines and give their x-intercept.

Objective The student will be able to: solve systems of equations by graphing.

Do Now 1) 2). Systems of Equations - Graphing System of Equations – two or more equations together. On the graph, the solution to a system of linear equations.

Objective: To solve a system of linear equations by graphing and substitution.

Solving Systems of Linear Equations in 2 Variables Section 4.1.

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)

Lesson 9.6 Topic/ Objective: To solve non linear systems of equations. EQ: How do you find the point of intersection between two equations when one is.

Systems of Linear Equations

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

EXAMPLE Determine whether the given point is a solution of the following system. point: (– 3, 1) system: x – y = – 4 2x + 10y = 4 Plug.

Systems of linear equations

ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.

Solving Equations with Variables on Both Sides

8.7Systems of Linear Equations – Part 1

Linear Systems November 28, 2016.

Chapter 5: Systems of Linear Equations

System of Equations Using Elimination.

Warm - Up Graph each equations on its own coordinate plane.

Systems of Equations Solving by Graphing.

5.1 Graphing Systems of Equations

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 3-1 and 3-2 (Solving Systems of Equations) ALGEBRA II SECTIONS 3-1 and 3-2.

Warm - Up Graph: 4x – 3y = 9.

7.1 System of Equations Solve by graphing.

6-1 Solving Systems by Graphing

Solve Systems of Equations

Do Now 1/18/12 In your notebook, explain how you know if two equations contain one solution, no solutions, or infinitely many solutions. Provide an example.

Systems of Equations Solving by Graphing.

9.6 Solving Systems of Equations by Graphing

Chapter 3 Section 1 Systems of Linear Equations in Two Variables All graphs need to be done on graph paper. Four, five squares to the inch is the best.

Solve Special Types of Linear Systems

System of Linear Equations:

Activating Prior Knowledge –

Systems of Equations Solving by Graphing.

Systems of Linear Equations: An Introduction

Solving Systems Using Elimination

3.1 Graphing Systems of Equations

11.6 Systems of Equations.

Objective: Students will solve systems by graphing

7.5 Special Types of Linear Systems

Systems of Linear Equations

Presentation transcript:

Lesson 5.4 The 3 kinds of systems Objective: To identify three types of linear systems. EQ: How can you tell the number of solutions of a system of equations? The 3 kinds of systems Regular system. When the two lines intersect once. One solution No Solution. When the lines never intersect (Parallel) No solutions 3) Coinciding lines. The two equations form the same line on top of each other. The same line. Every point that is true for one line is true for the other Infinite number of solutions

Samples One solution where the lines cross No solution the lines are parallel The lines coincide. All points that are true for one line are also true for the other. Many solutions Inconsistent Dependent

Example: Solve the system if possible 2x + 2y = 4 -x - y = -2 Multiply by 2 2x + 2y = 4 2x + 2y = 4 2(-x - y = -2) -2x – 2y = -4 0 = 0 Everything cancels These equations represent the same line. The system has an infinite number of solutions.

Example Solve if possible Multiply by 2 -x + y = 7 2x – 2y = -18 0 = –4 False ! No Solution These equations represent parallel lines

A Chemist needs to make 30 ounce of a 25% sodium solution by mixing together a 15% sodium solution and a 40% sodium solution. How much of each solution should they use. Mult by -.15 -.15( ) X + Y = 30 we need 30oz X 15% sodium .15 X + .4Y = 7.5 15% blended with 40% -.15X – .15Y = -4.5 Y 40% sodium .25Y = 3 30(.25) = 7.5 30oz of 25% .25 .25 Y = 12 12oz of 40% sodium solution X = 18 18 oz of 15% sodium solution 30 ounces of a 25% sodium solution