3.1 Graphing Systems of Equations Objective – To be able to solve and graph systems of linear equations. State Standard – 2.0 Students solve systems of linear equations by graphing Extra Example 1 Check whether (a) (1,4) and (b) (-5,0) are solutions of the following system. x – 3y = -5 -2x + 3y = 10 (a) (1) – 3(4) = -2(1) + 3(4) = 1 – 12 = = – Not a solution (b) (-5) – 3(0) = -2(-5) + 3(0) = – 5 10 Yes it is a solution

–5–4–3–2– –5 –4 –3 –2 – Extra Example 2 Solve the system graphically. 2x – 2y = -8 2x + 2y = 4 2x – 2y = -8 -2x -2y = -2x – 8 y = x + 4 2x + 2y = 4 2y = -2x + 4 y = -x x -2x Solution: (-1,3)

Number Of Solutions Of A Linear System infinitely many solutions (the graph is a single line.) (lines that intersect at one point.) exactly one solution no solution (lines are parallel) (Independent) (Dependent) (Inconsistent)

Extra Example 3 Tell how many solutions the linear system has. a) 2x + 4y = 12b) x – y = 5 x + 2y = 62x – 2y = 9 2x + 4y = 12 x + 2y = 6 x + 2y = 6 x – y = 5 2x – 2y = 9 -y = -x + 5 y = x –5 -x -x Infinitely many solutions -2x -2x -2y = -2x y = x – 9 / 2 No solutions

Guided Practice Due Today: Worksheet Activity

HOMEWORK Due Monday: Pg. 122 – – 9, 13, 14, 16, and 25 – 27 *For #’s 13, 14, and 16 state if it has one solution, infinitely many solutions, or no solution