1. Warm-Up 5 minutes Write each equation in slope-intercept form.
1) x – y = 9
2) 2x = 5y
3) 4x + 7y = 14 4) 5)

2. 3.1.1 Solving Systems by Graphing or Substitution
Objectives:
Solve a system of linear equations in two variables by graphing

3. Activity With your partner:
Partner 1 - graph the equation 2x + 3y = 12
Partner 2 - assist partner 1
Partner 2 - graph the equation x – 4y = -5
Partner 1 - assist partner 2
How many points of intersection are there? 1

4. Activity With your partner: Partner 1 - graph the equation x = 2y + 1
Partner 2 - assist partner 1
Partner 2 - graph the equation 3x – 6y = 9
Partner 1 - assist partner 2
How many points of intersection are there?

5. Activity With your partner: Partner 1 - graph the equation 2x = 4 - y
Partner 2 - assist partner 1
Partner 2 - graph the equation 6x + 3y = 12
Partner 1 - assist partner 2
How many points of intersection are there?
an infinite number

6. Classifying Systems of Equations
consistent: at least one solution
independent: exactly one solution
dependent: infinite number of solutions
inconsistent: no solution

7. Example 1
Graph and classify each system. Then find the solution from the graph. -8 -6 -4 -2 2 4 6 8
(1,1)
consistent,
independent

8. Example 2 inconsistent no solution
Graph and classify each system. Then find the solution from the graph.
inconsistent
no solution
let’s examine this graph with our calculators

9. Practice Solve by graphing. x + 4y = -6 2x – 3y = -1 y + 2x = 5

10. Homework
p.161 #11-23 odds
USE GRAPH PAPER

11. 6 minutes
Warm-Up
Graph and classify the system. Then find the solution from the graph.

12. 3.1.2 Solving Systems by Graphing or Substitution
Objectives:
Solve a system of linear equations by substitution

13. Example 1 (2,6) Solve using substitution. y = 3x 2x + 4y = 28

14. Example 2 Solve using substitution. 7x + y = 6 -7x -7x y = -7x + 6
= -3
7x + y = 6
5x + 7x – 6 = -3 7
+ y
= 6
12x – 6 = -3
12x = 3

15. Example 3 Solve using substitution. x – y + 4 = -4 x – y = -8
– 3( ) -4
= 7
6z = -24
z = -4
5x + 2x = 7
7x + 28 = 7
7x = -21
x = -3

16. Practice
Solve using substitution.

17. Homework
p.161 #27,29,31,39,41,45