Solving Linear Systems by Graphing

Key Terms: A system of two linear Equations – in ____ variables x and y, consist of two linear equations. Solution – consist of an order pair_____ . Two Types: Consistent – At least one Solution Independent – _______ ______ Dependent – ___________ ________ Inconsistent – No Solution

Consistent Vs. Inconsistent

Example: Exactly One Solve by Graphing. Check algebraically y = -1 3x + y = 5 Solution: ( )

CHECK Equation 1 Solution Equation 2 y = -1 (2, -1) 3x + y = 5 (-1) = -1 3(2) + (-1) = 5 -1 = -1 6 - 1 = 5 5 = 5

Example: Many Solutions Solve the system and Classify. y = 2x -1 -6x + 3y = -3

Example: No Solution 2x + y = 4 y = -2x +1

You Try It!!! Solve by Graphing and Check Algebraically y = -3x + 2 y = 2x - 3 4x + y = 5 y = -4x - 2 Solution: ( )

Homework Workbook - Page 36 & 37 # 1-12