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,

Slides:

Advertisements

Similar presentations

L ESSON 30 – I NTERSECTION OF L INES September 10, 2013 Fernando Morales.

Advertisements

1/4/2009 Algebra 2 (DM) Chapter 7 Solving Systems of Equations by graphing using slope- intercept method.

Solving System of Equations Using Graphing

Chapter 3 – Linear Systems

5.3 Systems of Linear Equations in Three Variables

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

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

Topic: Solving Systems of Linear Equations by Graphing.

Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic.

Advanced Algebra Notes

Sullivan Algebra and Trigonometry: Section 12.1 Systems of Linear Equations Objectives of this Section Solve Systems of Equations by Substitution Solve.

Section 3.5 Systems of Equations. What is a system of equations? Two or more equations in the same variables.

SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.

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.

Systems of Linear Equations

1.3 The Intersection Point of Lines System of Equation A system of two equations in two variables looks like: – Notice, these are both lines. Linear Systems.

Chapter 7 Determine the Relationship of a System of Equations 1/4/2009 Algebra 2 (DM)

The cost of bowling at bowling alley A or B is a function of the number of games g. Cost A = 2.5g + 2 Cost B = 2g + 4 When are the costs the same?

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

Systems of Linear Equations. A system of linear equations is simply two or more lines graphed on the same graph. They are also called simultaneous linear.

3.1 WARM-UP Graph each of the following problems

infinitely many solutions

Flashback. 1.2 Objective: I can identify parallel and perpendicular lines and use their postulates. I can also find the perimeter of geometric figures.

Answer these:  1. If two lines intersect, how many solutions exist?  2. If a system of two linear equations has no solution, what is true of their graphs?

Notes Over 2.1 Graphing a Linear Equation Graph the equation.

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

. 5.1 write linear equation in slope intercept form..5.2 use linear equations in slope –intercept form..5.3 write linear equation in point slope form..5.4.

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

3.1 “Solving Linear Systems with Graphing”

Warm Up 1.) Find the x – intercept of the graph of y = |x + 1|. 2.) Express the cost C of x ball game tickets at a price of $18 per ticket.

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

Solve Linear Systems Algebraically Part I Chapter 3.2.

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

Section 9.3 Systems of Linear Equations in Several Variables Objectives: Solving systems of linear equations using Gaussian elimination.

Solving Systems of Equations

3.1 Graphing Systems of Equations Objective – To be able to solve and graph systems of linear equations. State Standard – 2.0 Students solve systems of.

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.

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.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

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.

3.1 Solve Linear Systems by Graphing Algebra II. Definition A system of two linear equations in two variables x and y, also called a linear system, consists.

Algebra 2 Chapter 3 Review Sections: 3-1, 3-2 part 1 & 2, 3-3, and 3-5.

Chapter 3: Linear Systems and Matrices

Parallel Lines and Slope

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

Slope Intercept form. Geometry Unit 2-3, 2-4 Equations of lines Parallel and perpendicular slopes.

Systems of Equations and Inequalities

7.4 - The Intersection of 2 Lines

8.7Systems of Linear Equations – Part 1

Linear Systems November 28, 2016.

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

Movable lines class activity.

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

Lesson 3-6: Perpendicular & Distance

Systems of Equations Solving by Graphing.

5.1 Graphing Systems of Equations

7.1 System of Equations Solve by graphing.

Writing Linear Equations Given Two Points

Solve Systems of Equations

Systems of Equations Solving by Graphing.

9.6 Solving Systems of Equations by Graphing

SECTION 6-1 : SOLVING SYSTEMS WITH 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

Geometry Section 3.5.

System of Linear Equations:

Systems of Linear Equations: An Introduction

7.1 Solving Systems of Equations

Parallel and Perpendicular Lines

3.5 Write and Graph Equations of Lines

Presentation transcript:

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, or infinitely many solutions. Geometrically, this means :  Intersecting Lines Parallel Lines Coincident Lines

Postulate 12  If two distinct lines intersect, then their intersection is exactly one point. (think systems of equations)

Postulate 13 Parallel Postulate  If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. b ● a

Example: Line 1 is given by Line 2 is parallel to Line 1 and passes through the point (3,2). Write the equation for Line 2.

Example 2: is given by is parallel to and passes through the point (1,-1). Write the equation for.

Postulate 14 Perpendicular Postulate  If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. ● a

Example: Write the equation of the line which passes through (-1,3) and is perpendicular to Example 2: is given by is perpendicular to and passes through the point (5, -3). Write the equation for.

More Examples: 1. Solve the following system of equations: x – 2y = -7 3x + 4y = 9 2. Find the equation of a line that is parallel to y = -3x + 2 and passes through the point (2,1). 3. Find the equation of a line that is perpendicular to y = -2x + 1 and passes through the point (4,0).

More Examples: 4. Write the equation of the line through (-3,2) and (-1,-4). 5. Write in standard form. 6. Write the equation of the line through (-4,4) and (-2,-3) in standard form. 7. Write the equation of the line through (4,9) and (4,5). 8. Write the equation of the line through (-4,-1) and (12,-1).