Topic: U4L2 Solving Nonlinear Systems of Equations EQ: How can I solve a system of equations if one or more of the equations does not represent a line?

Slides:

Advertisements

Similar presentations

4.1 System of linear Equations Solving graphically Solving by substitution Solving by addition.

Advertisements

Chapter 5 Objectives 1. Find ordered pairs associated with two equations 2. Solve a system by graphing 3. Solve a system by the addition method 4. Solve.

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

UNIT 6.15 Special Solutions: Graphing I can identify special solutions within a system of equations graphically.

Solving System of Equations Using Graphing

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

Systems of Equations SPI Solve systems of linear equation/inequalities in two variables.

Objective - To graph linear equations using x-y charts. One Variable Equations Two Variable Equations 2x - 3 = x = 14 x = 7 One Solution.

Systems of Linear Equations

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

7.1 Graphing Linear Systems

The student will be able to:

Solving Systems of Equations: Elimination Method.

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

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.

I can solve systems of equations by graphing and analyze special systems.

CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.

Warm-Up 5 minutes 1) On the coordinate plane, graph two lines that will never intersect. 2) On the coordinate plane, graph two lines that intersect at.

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

Advanced Algebra Notes

3.1: Solving Linear Systems by Graphing Group 4.  Get two variables, (x,y), to correctly come out of two equations  ax+by=c  dx+ey=f  Check whether.

Substitution Method: 1. Solve the following system of equations by substitution. Step 1 is already completed. Step 2:Substitute x+3 into 2 nd equation.

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

5.2: Solving Systems of Equations using Substitution

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

Section 4.1 Systems of Linear Equations in Two Variables.

Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.

Solving Systems of Linear Equations by Substitution; Applications Solve systems of linear equations using substitution. 2.Solve applications involving.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

3.1 Solving Systems By Graphing Or Substitution. * A system of equations is a collection of equations in the same variable. *A solution to a system is.

Solving Systems of Equations Graphing Linear Inequalities.

Systems of Equations Section 6.1 Solve systems of linear equation/inequalities in two variables.

 How do I solve a system of Linear equations using the graphing method?

Solving Systems of Linear Equations in 2 Variables Section 4.1.

Systems of Equations Draw 2 lines on a piece of paper. There are three possible outcomes.

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.

Lesson 4-1 Solving linear system of equations by graphing

Objective I can solve systems of equations using elimination with addition and subtraction.

Systems of Linear Equations

Chapter 6 Conic Sections

Solving System of Linear Equations

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

SYSTEMS OF LINEAR EQUATIONS

Warm Up 3x + 5y = 25 4x + 7y = 34 Find the value of x and y so that both equations are true.

The student will be able to:

Solving Linear Systems Algebraically

Solve a system of linear equation in two variables

Systems of Linear Equations in Two Variables

Solve Systems of Equations

Systems of equations.

Solving Systems of non-linear Equations

Warm Up Solve each quadratic equation by factoring. Check your answer.

Chapter 11 Section 4.

9.6 Solving Systems of Equations by Graphing

If you can easily isolate one of the variables,

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.

Question How do you solve a system of simultaneous equations by substitution?

Indicator 16 System of Equations.

Objectives Identify solutions of linear equations in two variables.

5.1 Solving Systems of Equations by Graphing

that ordered pair is the one solution.

has one solution, it is the point where the lines intersect

All solutions of a linear equation are on its graph

Systems of Equations Solve by Graphing.

Warm Up Check to see if the point is a solution for the

11.6 Systems of Equations.

Solving Systems of Linear Equations by Substitution

Nonlinear Systems of Equations

Warm- Up: Solve by Substitution

Solving Linear Systems by Graphing

Presentation transcript:

Topic: U4L2 Solving Nonlinear Systems of Equations EQ: How can I solve a system of equations if one or more of the equations does not represent a line?

 System – 2 or more equations together  Solution of system – any ordered pair that makes all equations true  Possible solutions: 1. One point 2. More than one point 3. No solution 4. Infinite solutions Review – What?

Review - How?  What methods have we used to solve linear systems of equations? 1. Graphing 2. Substitution

Review Steps for using SUBSTITUTION 1. Solve one equation for one variable. (Hint: Look for an equation already solved for a variable or for a variable with a coefficient of 1 or -1.) 2. Substitute into the other equation. 3. Solve this equation to find a value for the variable. 4. Substitute again to find the value of the other variable. 5. Check.

Review Solve using Substitution. 2x – y = 6 y = 5x

What’s New?  A non-linear system is one in which one or more of the equations has a graph that is not a line.  With non-linear systems, the solution could be one or more points of intersection or no point of intersection.  We’ll solve non-linear systems using substitution.  A graph of the system will show the points of intersection.

 Solve the following system of equations : An Example…

 We use the substitution method. First, we solve equation (2) for y.

An Example…  Next, we substitute y = 2x  3 in equation (1) and solve for x:

An Example… …  Now, we substitute these numbers for x in equation (2) and solve for y.  x = 0x = 12 / 5 y = 2x  3 y = 2(0)  3 y = 3 SOLUTIONS (0, 3) and

An Example… Check: (0, 3) Check:  Visualizing the Solution

Example 1 Solve by substitution.  x 2 = y – 1  4x – y = -1

Example 2  Solve by substitution. x + 2y = 0 (x – 1) 2 + (y – 1) 2 = 5

Another example to watch…  Solve the following system of equations: xy = 4 3x + 2y = 10