1. + Special Linear Systems 7.5

2. + Previously… Consistent Independent System – exactly one solution

3. + Now… Inconsistent system – A linear system with no solution Consistent dependent system – A linear system with infinitely many solutions

4. + Inconsistent system/one solution 3x + 2y = 10 3x + 2y = 2 -1( ) 3x + 2y = 10 -3x - 2y = -2 0 = 8

5. + Consistent dependent/Infinite X – 2y = -4 Y = (1/2)x + 2 X – 2[(1/2)x + 2] = -4 x – x – 4 = -4 x – x = 0 0 = 0

6. + Examples Tell whether the linear system has no solution or infinitely many solutions. 5x + 3y = 6 -5x – 3y = 3 Y = 2x – 4 -6x + 3y = -12

7. + Try it out Tell whether the linear system has no solution or infinitely many solutions. 4x – 2y = 8 Y = 2x – 4 2x – 3y = 6 2x – 3y = -4

8. + Helpful Hint IF the equations are in slope-intercept… Number of SolutionsSlope/y-intercept One solutionDifferent slopes No solutionSame slope Different y-intercepts Infinitely many solutionsSame slope Same y-intercept

9. + Without solving Tell how many solutions the linear system has. 5x + y = -2 -10x – 2y = 4 6x + 2y = 3 6x + 2y = -5

10. + You try -3x + 5y = 6 6x – 10y = -12 9x – 5y = 12 9x – 5y = 8