Lesson 3.1 Graphing Systems.notebook
October 24, 2011
3.1
Graphing Systems of Equations
Objective:
Be able to solve systems of equations using graphing
Oct 19­7:44 AM
Systems of Equations
Definition:
Three Ways to Solve:
1. Graphing
{
y = x + 3
y = ­2x + 3
2. Elimination
3. Substitution
Oct 20­8:20 AM
1
Lesson 3.1 Graphing Systems.notebook
October 24, 2011
{
y = x + 3
y = ­2x + 3
Oct 19­7:49 AM
{
Which ordered pair of numbers is
the solution to the system?
x + 2y = ­7
2x ­ 3y = 0
a. (1, ­4)
Graph to check
b. (­1, ­3)
c. (­6, ­4)
d. (­3,­2)
Oct 20­8:42 AM
2
Lesson 3.1 Graphing Systems.notebook
October 24, 2011
3 Types of systems
1. Independent 2. Dependent
slope:
y-intercept:
solution:
3. Inconsistent
slope:
slope:
y-intercept:
y-intercept:
solution:
solution:
Oct 20­8:47 AM
Without graphing, classify each system as
independent, dependent or inconsistent
{
{
3x + y = 5
y ­ 3x = 2
­6x + 2y =4
15x ­ 2 = ­5y
Oct 20­8:54 AM
3
Lesson 3.1 Graphing Systems.notebook
October 24, 2011
Graph the system to find the
solutions. Check your answers.
x + 3y = 2
{
3x +3y = ­6
Oct 20­9:07 AM
{
10 ­ 3x = ­3y
2 = 2x + y
Oct 20­9:10 AM
4
Lesson 3.1 Graphing Systems.notebook
October 24, 2011
3.2
Solving Systems Algebraically
Objectives:
• Be able to solve a system of equations by elimination
• Be able to solve a system of equations by substitution
Oct 22­8:54 AM
Elimination
{
4x ­ 2y = 7
x + 2y = 3
Step 1: Arrange the equations in standard form
Step 2: Circle the terms you want to eliminate. (Look for coefficients that are opposites)
Step 3: Multiply each term of one or both equations by an appropriate number so the coefficients are opposites
Step 4: Add the equations
Step 5: Substitute the value obtained in step 4 into either of the original equations and solve for the other variable.
Step 6: Check the solution in the original equation
Oct 22­9:52 AM
5
Lesson 3.1 Graphing Systems.notebook
October 24, 2011
Elimination
{
2x + 4y = ­4
3x + 5y = ­3
Oct 22­10:02 AM
Homework #18
Pg. 120 #1-6(by hand), 13-18,
25-28(can use calculator)
Oct 20­9:11 AM
6