Ordered pairs ( x , y ) as solutions to Linear Equations

Slides:

Advertisements

Similar presentations

Finding Equations of Exponential Function

Advertisements

Solve a System Algebraically

5-1 Solving Systems by Graphing

Table of Contents First, find the least common denominator (LCD) of all fractions present. Linear Equations With Fractions: Solving algebraically Example:

Vocabulary Chapter 6.

THE ELIMINATION METHOD Solving Systems of Three Linear Equations in Three Variables.

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.

Solving System of Equations Using Graphing

Table of Contents Solving Linear Systems of Equations - Substitution Method Recall that to solve the linear system of equations in two variables... we.

EXAMPLE 3 Write an equation for a function

7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.

3.5 Solving systems of equations in 3 variables

5.3 Solving Systems using Elimination

7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.

Solving Equations Containing To solve an equation with a radical expression, you need to isolate the variable on one side of the equation. Factored out.

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

Solving Systems of Equations: Elimination Method.

Solving Linear Systems Substitution Method Lisa Biesinger Coronado High School Henderson,Nevada.

Table of Contents First note this equation has "quadratic form" since the degree of one of the variable terms is twice that of the other. When this occurs,

GRAPH LINEAR INEQUALITIES IN TWO VARIABLES January 22, 2014 Pages

Section 4-1: Introduction to Linear Systems. To understand and solve linear systems.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

Solving a System of Equations by SUBSTITUTION. GOAL: I want to find what x equals, and what y equals. Using substitution, I can say that x = __ and y.

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.

Solving Linear Systems of Equations - Substitution Method Recall that to solve the linear system of equations in two variables... we need to find the value.

Warm Up Evaluate each expression for x = 1 and y =–3. 1. x – 4y 2. –2x + y Write each expression in slope-intercept form, then then graph. 3. y – x = 1.

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?

Linear Equations in Two Variables A Linear Equation in Two Variables is any equation that can be written in the form where A and B are not both zero.

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Solving Linear Equations Substitution. Find the common solution for the system y = 3x + 1 y = x + 5 There are 4 steps to this process Step 1:Substitute.

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

Solving Linear Systems of Equations - Concept Consider the following set of equations: Such a set is called a Linear System of Equations in two variables.

Solving Linear Systems by Substitution

Differential Equations Linear Equations with Variable Coefficients.

SYSTEMS OF EQUATIONS. SYSTEM OF EQUATIONS -Two or more linear equations involving the same variable.

Key Concepts for Sect. 7.1 *A system of equations is two or more equations in two or more variables. *Numerically, a solution to a system of equations.

6-2 SOLVING LINEAR SYSTEMS BY SUBSTITUTION Goal: Use substitution to solve a linear system Eligible Content: A / A

6.5 Solving Exponential Equations SOLVE EXPONENTIAL EQUATIONS WITH THE SAME BASE. SOLVE EXPONENTIAL EQUATIONS WITH UNLIKE BASES.

Solving Systems by Substitution (isolated) Solving Systems by Substitution (not isolated)

5.1 Solving Systems of Linear Equations by Graphing

Warm-Up Solve the system by graphing y = x + 2 x = −3 Solve the system by graphing 4x + y = 2 x − y = 3.

Lesson 4-1 Solving linear system of equations by graphing

X.2 Solving Systems of Linear Equations by Substitution

Solve Linear Systems by Graphing

Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y

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

Solve Quadratic Systems

Solve a system of linear equation in two variables

Lesson 7-4 part 3 Solving Systems by Elimination

3.5 Solving systems of equations in 3 variables

Solving Systems of Equations using Substitution

Systems of Linear Equations in Two Variables

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

3.2a – Solving Systems algebraically

Systems of Linear and Quadratic Equations

Before: December 4, 2017 Solve each system by substitution. Steps:

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

Function - when every x is paired to one y

6-2 Solving Linear Systems by substitution

If you can easily isolate one of the variables,

Chapter 4 – Linear Systems

Objectives Identify solutions of linear equations in two variables.

Systems of Equations.

7.1 solving linear systems by graphing

6.3 Using Elimination to Solve Systems

Chapter 8 Systems of Equations

Finding Equations of Exponential Function

Chapter 9 Lesson 4 Solve Linear Systems By Substitution

Tell whether the ordered pair is a solution of the equation.

Warm- Up: Solve by Substitution

Presentation transcript:

Ordered pairs ( x , y ) as solutions to Linear Equations Here are some examples of Linear Equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations.

Ordered pairs ( x , y ) as solutions to Linear Equations Here are some examples of Linear equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations. Every solution of a Linear equation is an ordered pair of numbers, x and y. This pair, when substituted into the equation, creates an equality. If no equality exists, the ordered pair IS NOT a solution.

STEPS : 1. Substitute the given ( x , y ) into the equation. Ordered pairs ( x , y ) as solutions to Linear Equations Here are some examples of Linear equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations. Every solution of a Linear equation is an ordered pair of numbers, x and y. This pair, when substituted into the equation creates an equality. If no equality exists, the ordered pair IS NOT a solution. STEPS : 1. Substitute the given ( x , y ) into the equation. 2. Check to see if an equality exists.

Substitute x = 2, and y =3 into the equation. EXAMPLE : Substitute x = 2, and y =3 into the equation.

Substitute x = 2 , and y = 3 into the equation. EXAMPLE : Substitute x = 2 , and y = 3 into the equation.

Substitute x = 2 , and y = 3 into the equation. EXAMPLE : Substitute x = 2 , and y = 3 into the equation. Since this creates an equality, the given point IS a solution to the equation.

EXAMPLE :

EXAMPLE : Substitute x = - 4 , and y = 7 into the equation.

EXAMPLE : Substitute x = - 4 , and y = 7 into the equation. Since the equality doesn’t exist, the given ordered pair IS NOT a solution to the equation.

You try one. See if you can get the solution first without seeing how I did it.

You try one. See if you can get the solution first without seeing how I did it.

You try one. See if you can get the solution first without seeing how I did it. Substitute x = 3 and y = 9 into the equation

You try one. See if you can get the solution first without seeing how I did it. Substitute x = 3 and y = 9 into the equation Since an equality exists, the ordered pair IS a solution to the equation.

PRACTICE Complete the following problems. You can check your answers in the solution bank. Test each ordered pair and see if it is a solution to the given equation.

PRACTICE Complete the following problems. You can check your answers in the solution bank. Test each ordered pair and see if it is a solution to the given equation.