Wednesday: Factoring Warm-up Find the factors and solutions

Solving Linear Systems Algebraically with Substitution and Elimination Section 3-2 Pages

Objectives I can use the Substitution Method to solve systems of equations I can use the Elimination Method to solve systems of equations

Substitution Method Goal 1. Isolate one variable in one equation 2. Substitute into the other equation(s) AWAYS pick the easiest equation to isolate.

Which Equation to Isolate

Example 1

What does it mean? When we found the solution (6, -1) What does that really mean??? Intersection of the 2 graphs!!

y=-2/5x+7/5 y=-1/4x+1/2 (6, -1)

Your Turn! Solve by Substitution #1 Homework

Example 2

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.

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 couple

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

Example 1

Your Turn #5 Homework 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 (2 nd, 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 Variables are gone and you get this: 2x + 3 = 2x – 4 3 = -4 This is not possible, so No Solution Infinite Solutions Variables are gone and you get this: 2x + 3 = 2x = 3 This is always true, so Infinite Solutions

Homework WS 6-2 Quiz Next Class