Lesson 7.5

Objective: To identify three types of linear systems

The 3 kinds of systems1) Regular system. When the two lines intersect once. One solution2) No Solution. When the lines never intersect (Parallel) No solutions

3) Coinciding lines. The two equations form the same line on top of each other. The same line. Every point that is true for one line is true for the other

Infinite number of solutions

Samples

One solution where the lines cross

No solution the lines are parallel

The lines coincide. All points that are true for one line are also true for the other. Many solutionsInconsistent

Dependent

Example: Solve the system if possible

2x + 2y = 4

-x - y = -2

2x + 2y = 4

2(-x - y = -2)

Multiply by 2

2x + 2y = 4

-2x – 2y = -4

0 = 0 Everything cancels

These equations represent the same line. The system has an infinite number of solutions.

Example Solve if possible

-x + y = 7

2x – 2y = -18

Multiply by 2

2(-x + y = 7)

2x – 2y = -18

-2x + 2y = 14

2x – 2y = -18

0 = –4 False !

No Solution

These equations represent parallel lines