1. Lesson 7.5 Objective: To identify three types of linear systems The 3 kinds of systems 1)Regular system. When the two lines intersect once. One solution 2)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

2. 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 solutions Inconsistent Dependent

3. 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.

4. 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