System of Equations Elimination Method

Slides:

Advertisements

Similar presentations

Part 2.  Review…  Solve the following system by elimination:  x + 2y = 1 5x – 4y = -23  (2)x + (2)2y = 2(1)  2x + 4y = 2 5x – 4y = -23  7x = -21.

Advertisements

Solve each with substitution. 2x+y = 6 y = -3x+5 3x+4y=4 y=-3x- 3

Solving Systems Using Elimination Objective: To solve systems of equations algebraically.

3.2 Solving Systems of Equations Algebraically Substitution Method Elimination Method.

Graphing Systems of Equations Graph of a System Intersecting lines- intersect at one point One solution Same Line- always are on top of each other,

SOLVING SYSTEMS of EQUATIONS MATH REVIEW. Suppose… … you want to solve a set of two linear equations: y = 5z – 4 and y = -4z + 2. There are two methods.

Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.

6-3: Solving systems Using Elimination

Ch 5.4 (part 2) Elimination Method (multiplying both equations)

Chapter 4.1 Solving Systems of Linear Equations in two variables.

Systems of Equations: Elimination, Part II Unit 7, Lesson 5b.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

Solution Because no variable appears in the denominator, no restrictions exist. The LCM of 5, 2, and 4 is 20, so we multiply both sides by 20: Example.

Solving Systems of Equations using Elimination. Solving a system of equations by elimination using multiplication. Step 1: Put the equations in Standard.

Solving Systems of Equations Algebraically Chapter 3.2.

Solving Systems Using Elimination

Solve the following system using the elimination method.

Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination.

Notes – 2/13 Addition Method of solving a System of Equations Also called the Elimination Method.

7.4. 5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. In this linear.

Lesson 2.8 Solving Systems of Equations by Elimination 1.

Objective: To solve multi-step inequalities Essential Question: How do I solve multi-step inequality? Example #1 : solving multi-step inequalities 2x −

Solving Systems of Equations by Elimination. Standard and Objective A.REI.5 Prove that, given a system of two equations in two variables, replacing one.

Systems of Equations By Dr. Marinas. Solving Systems Graphing Method Substitution Method Elimination (or Adding) Method.

Lesson 1.  Example 1. Use either elimination or the substitution method to solve each system of equations.  3x -2y = 7 & 2x +5y = 9  A. Using substitution.

Multi Step Equations. Algebra Examples 3/8 – 1/4x = 1/2x – 3/4 3/8 – 1/4x = 1/2x – 3/4 8(3/8 – 1/4x) = 8(1/2x – 3/4) (Multiply both sides by 8) 8(3/8.

Systems of Equations By Substitution and Elimination.

Elimination using Multiplication Honors Math – Grade 8.

Martin-Gay, Beginning Algebra, 5ed Solve the following rational equation.EXAMPLE Because no variable appears in the denominator, no restrictions.

Objective The student will be able to: solve systems of equations using elimination with addition and subtraction.

Algebra 2 Solving Systems Algebraically Lesson 3-2 Part 2.

The student will be able to:

HW: Maintenance Sheet #21 (19-21) comprehensive Test 7 Friday

Solving Systems of Equations using Substitution

Solving Systems of Equations

Objective I CAN solve systems of equations using elimination with multiplication.

Solving Systems of Two Equations

Learning Target I can solve and graph multi-step, one-variable inequalities using algebraic properties.

Solving Multi-step Inequalities

Solve Systems of Equations by Elimination

Warm up Graph y = 3x – 4 y = -2x + 11 on your graphing calculator.

Solving Inequalities by Multiplying or Dividing

Solving Inequalities with Variables on Both Sides

Solving Systems using Substitution

Introduction Two equations that are solved together are called systems of equations. The solution to a system of equations is the point or points that.

Solving a system of equations by elimination using multiplication.

6-3 Solving Systems Using Elimination

Solving Systems Using Elimination

Solve Systems of Equations by Elimination

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

Solving systems of equations

Solving Equations Containing Decimals

Rational Expressions and Equations

Lesson 7.4 Solving by Multiplication

The student will be able to:

Objective Solve inequalities that contain variable terms on both sides.

Solving Systems of Equations

Algebra: Variables and Expressions

Evaluating Expressions and Solving Equations

Solving Systems of Two Equations

Solving Systems of Linear Equations by Elimination

SOLVING SYSTEMS OF EQUATIONS.

The student will be able to:

If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before.

Warm-Up # Is (–1, 4) a solution to

Systems of three equations with three variables are often called 3-by-3 systems. In general, to find a single solution to any system of equations,

Solving Systems of Equations:

SOLVING SYSTEMS OF EQUATIONS.

The student will be able to:

SOLVING SYSTEMS OF EQUATIONS.

Presentation transcript:

System of Equations Elimination Method Presented Mr. Laws 8th Math JCMS

Standard/Goal 8.EE.8a – Solve systems of equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Essential Questions Using math principles, how do I solve a system of equations using the elimination method?

What is the Elimination Method? The elimination method is used to solve system of equations by eliminating either the x or y variable of one equation. The both equations in the system is written in standard form.

Solving System by Elimination Example # 1 Step 1: Look for a variable you can eliminate in the system. x + 4y = 8 3x – 4y = 8 Step 2: Since there is positive 4y in the 1st equation and a negative 4y in the second equation, the y variable can be eliminated. 4x = 16 4 Step 3: Add the x variable: 1x + 3x = 4x; constant: 8 + 8 = 16 ( 4, 1) x = 4 Step 4: Solve for x 4 + 4y = 8 Step 5: Replace the value of x in one of the equations to find the value of y. -4 4y = 4 4 y = 1 Step 6: Solve for y

Solving System by Elimination Example # 2 Step 1: Can’t eliminate x or y, so pick an easy variable to eliminate: 2x + 5y = 9 x – 3y = 10 Step 2: Eliminate x in the second equation by multiplying the equation by -2: -2(x – 3y = 10) Step 3 : Eliminate the x variable and solve for y. -2x + 6y = - 20 2x + 5y = 9 11y = -11 11 y = -1 2x + 5 (-1) = 9 2x – 5 = 9 + 5 +5 2x = 14 2 2 x = 7 Step 4: Replace the value of y in one of the equations and solve for x. ( 7, -1)

Solving System by Elimination Step 1: Find the least common multiple (LCM) of one the variables. Example # 3 5x + 3y = 2 4x + 2y = 10 Step 2: LCM of 3 (y) and 2 (y) = 6 Multiply the 1st equation by -2 and the 2nd equation by 3 to eliminate the y variable. -2(5x +3y = 2) 3(4x +2y = 10) Step 3 : Use the distributive property to change both equations. -10x – 6y = -4 12x + 6y = 30 5(13) + 3y = 2 Step 4 : Eliminate the y variable and solve for x. 65 + 3y = 2 -65 -65 Step 5: Replace the value of x in one of the equations and solve for y. 2x = 26 2 2 3y = -63 3 3 y = -21 x = 13 ( 13, -21)

Summary What have you learn in this lesson? What are some important things to remember about system of equations? Do you have additional questions concerning this lesson?