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.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Write an equation of a line from a graph

Advertisements

5-1 Solving Systems by Graphing

Solving Special Systems

Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

SOLVING SYSTEMS USING SUBSTITUTION

Step 1: Simplify Both Sides, if possible Distribute Combine like terms Step 2: Move the variable to one side Add or Subtract Like Term Step 3: Solve for.

Solving Systems of Linear Equations and Inequalities

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

Solving Systems of Linear Equations by Graphing

ALGEBRA II SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. 2. Two lines in the same plane are if they do not intersect. ? ? The least common.

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

Systems of Linear Equations Method 1: Using a Graph to Solve Method 2 : Solve by Substitution Method 3 : Solve by Linear Combination / Elimination.

Solving Systems Using Elimination

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

Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 Text p. 462, #1-8 all, #10, #12, #16-30.

 What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4)  Identify the slope and y -intercept of each equation. 2.y.

Systems of Equations Standards: MCC9-12.A.REI.5-12

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

Good Morning, We are moving on to chapter 3. If there is time today I will show you your test score you can not have them back as I still have several.

A system of two linear equations in two variables represents two lines. The lines can be parallel, intersecting, or coinciding. Lines that coincide are.

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.

Warm Up Tell whether the system has one solution, no solution, or infinitely many solutions.

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

Systems of Equations. OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination.

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

Ch. 3 Notes 3.1 – 3.3 and 3.6.

Systems of Equations Substitution Elimination Inequalities Systems of Inequalities Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.

Classifying Systems, Solving Systems by Graphing and Substitution

Solve by Graphing Solve: 3x + 4y = - 4 x + 2y = 2

1. The square root of 9 is 3 True

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.

Special Types of Linear Systems

Solving Systems of Linear Equations and Inequalities

Warm Up Evaluate each expression for x = 1 and y =–3.

Solving Systems of Linear Equations in Three Variables

Chapter 5: Systems of Linear Equations

6-2 Solving Systems using Substitution

Systems of Equations Solving by Graphing.

Solve a system of linear equation in two variables

The equation of a line can be written in many different forms

6-1 Solving Systems by Graphing

Lesson 7.1 How do you solve systems of linear equations by graphing?

Solve Linear 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.

Graph the equation..

infinitely many solutions

Systems of Equations Solving by Graphing.

Solving Special Systems

There are infinite solutions to the system.

Chapter 4 – Linear Systems

Objectives Identify solutions of linear equations in two variables.

SYSTEMS OF LINEAR EQUATIONS

Chapter 8 Systems of Equations 8.1 Solve Systems by Graphing

Systems of Equations Solve by Graphing.

Objectives Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding.

Graphing Systems of Equations

Solving Systems Using Elimination

7.1 Solving Systems of Equations

11.6 Systems of Equations.

Lesson 0 – 8 Systems of Linear Equations

Solving Linear Systems by Graphing

Presentation transcript:

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 linear system. METHOD 1 Graphing

EXAMPLE 1 A linear system with no solution ANSWER The lines are parallel because they have the same slope but different y- intercepts. Parallel lines do not intersect, so the system has no solution.

EXAMPLE 1 A linear system with no solution ANSWER The variables are eliminated and you are left with a false statement regardless of the values of x and y. This tells you that the system has no solution. Subtract the equations. METHOD 2 Elimination 3x + 2y = 10 3x + 2y = 2 0 = 8 This is a false statement.

EXAMPLE 2 A linear system with infinitely many solutions Show that the linear system has infinitely many solutions. x – 2y = –4 Equation 1 Equation 2 y = x SOLUTION Graphing METHOD 1 Graph the linear system.

EXAMPLE 2 A linear system with infinitely many solutions ANSWER The equations represent the same line, so any point on the line is a solution. So, the linear system has infinitely many solutions.

EXAMPLE 2 A linear system with infinitely many solutions Substitute x + 2 for y in Equation 1 and solve for x. 1 2 x – 2y = –4 Write Equation 1. 2 Substitute x + 2 for y. 1 x – 2 x + 2 = 1 2 –4 METHOD 2 Substitution The variables are eliminated and you are left with a statement that is true regardless of the values of x and y. This tells you that the system has infinitely many solutions. ANSWER –4 = –4 Simplify.

GUIDED PRACTICE for Examples 1 and x + 3y = 6 –5x – 3y = 3 Tell whether the linear system has no solution or infinitely many solutions. Explain. ANSWER No solution. Sample answer: When you solve the system you get 0 = 9, which is a false statement.

GUIDED PRACTICE for Examples 1 and 2 2. y = 2x – 4 –6x + 3y = –12 Tell whether the linear system has no solution or infinitely many solutions. Explain. ANSWER Infinitely many solutions. Sample answer: When you solve the system you get  12 =  12, which is a true statement.