This document summarizes special types of linear systems. It discusses investigating different types of linear systems using a graphing calculator activity. There are three different solutions to linear systems: 1) lines intersect with one solution, 2) lines are parallel and have no solution (inconsistent system), and 3) lines coincide with infinitely many solutions (consistent dependent system). Students are assigned problems 1 through 12 on page 463 to practice determining the different types of solutions to linear systems.

1. Special Types of Linear
Systems
Section 7.5
P. 459-463

2. • Today we are going to start with a
graphing calculator activity to investigate
special types of linear systems.

3. • Write each pair in the form y = mx + b
• Graph each pair (one pair at a time) on the
same coordinate plane.
• Determine how many different “types” of
linear systems there are.
• Be prepared to explain your results.

4. Slope – Intercept Form
• A) x + y = 9 3x – 2y = 10
• B) 2x – 4y = 6 x – 2y = 3
• C) x – y = 1 -3x + 3y = 3

5. • A) y = -x + 9 y = 3/2 x – 5
• B) y = 2/4 x – 6/4 y = ½ x – 3/2
• C) y=x–1 y=x + 1

6. • There are 3 different solutions to linear
systems
1. Lines intersect with ONE solution
2. Lines are parallel and have NO
SOLUTION (inconsistent system)
3. Lines COINCIDE – infinitely many
solutions (consistent dependent system)

7. • How could you show this linear system
has no solution?
• - 6x + 2y = -8
• - 3x + y = 7

8. Show that this linear system has infinitely
many solutions
- x + 2y = - 2 3x – 6y = 6

9. Assignment
• Do P. 463 1-12