1. Algebra 7.5 Special Types of Linear Systems

2. Solve the Linear System -4x + 2y = 6 -2x + y = 3 4x - 2y = -6 0 = 0 0 = 0 What does this mean? The final equation is true! There are infinite solutions!! How could this be? We will answer this shortly. [ ]-2

3. Solve the Linear System y = 3x + 7 -6x + 2y = -8 -6x + 2(3x + 7) = -8 -6x + 6x + 14 = -8 14 = -8 14 = -8 What does this mean? The final equation is false! There is no solution!! How could this be? We will answer this shortly. ( )

4. How many solutions? One solution.No solution. Infinite Solutions.

5. 3x + y = -1 -9x – 3y = 3 -2x + 4y = 2 x = 2y + 5 6x + 3y = 12 4x – 2y = 0 a)c)b) [ ]3 9x + 3y = -3 0 = 0 Infinite Solutions. ( ) -2(2y + 5) + 4y = 2 -4y – 10 + 4y = 2 -10 = 2 No solution. [ ]2 [ ]3 12x + 6y = 24 12x – 6y = 0 24x = 24 x = 1 6(1) + 3y = 12 6 + 3y = 12 3y = 6 y = 2 One solution: (1, 2)

6. A Few From the HW Together P. 430 #27, #30 P. 429 #A P. 430 #27, #30 P. 429 #A

7. HW P. 429 #12-32, #36-37 P. 429 #12-32, #36-37