Warm-up Solve the first system of equations by the Substitution Method, then graphing

Solving Linear Systems Algebraically with Elimination Section 3-2 Pages 160-1-67

Objectives I can use the elimination method to solve equations I can set up and solve word problems using elimination

Elimination Method GOAL 1. Add the equations together and have one variable term go away. 2. Sometimes you will have to multiply one or both equations by a number to make this happen.

Example 1 Now, PLUG this back into Either equation to find “y”

It is ALWAYS an Ordered Pair What does this mean? Remember that a solution to a system of equations is where the graphs cross It is ALWAYS an Ordered Pair

Multiplying by a number? Many times you cannot add the equations and have a variable term cancel For these cases, you must multiply One or Both equations by a number first Let’s look at a few

What to Multiply by? x-variable will cancel y-variable will cancel

Example 2

Your Turn Solve the following system of equations using elimination:

Other Methods Remember, the solution to a system of equations if an ordered pair You know 2 other methods to check your answers: Graphing Calculator and asking for the intersection (2nd, Trace, Intersection, E, E, E) Substitution Method

Solution Types Remember there are 3 types of solutions possible from a system of equations!

No Solution vs Infinite How will you know if you have No Solution or Infinite Solutions when solving by Substitution??

Remember Back to Solving Equations No Solution Infinite Solutions Variables are gone and you get this: 2x + 3 = 2x – 4 3 = -4 This is not possible, so No Solution Variables are gone and you get this: 2x + 3 = 2x + 3 3 = 3 This is always true, so Infinite Solutions

Word Problems When solving a word problem, consider these suggestions 1. Identify what the two variables are in the problem 2. Write equations that would represent the word problem, looking for key words Sum, difference, twice, product, half, etc…

Example 1 GEOMETRY: The length of a rectangle is 8 cm more than twice the width. If the perimeter is 40 cm, find the dimensions. Variables: Length (L) Width (W) Equations: L = 2W + 8 2L + 2W = P Now, solve by elimination

Example 2 Rental car agency A charges $8 per day plus $.20 per mile. Rental car company B charges $10, but only $.10 per mile. At what mileage is it better to use Company B? Cost (C) Miles (M) Equations: C = 8 + .20M C = 10 + .10M Now, solve by Elimination

Homework Elimination Worksheet