Stand Quietly

Lesson 5.4 Solving Special Systems of Linear Equations Students will be able to use method of graphing, substitution, and elimination to determine no solution, one solution, or many solutions on a systems of linear equations.

Warm-Up #16 (3/20/2017) Determine if the systems of equations have one solution, no solutions, or infinite solutions. 1. 𝑥+𝑦=2 2. 𝑥+ 3 5 𝑦=2 3. 3𝑥+𝑦=10 3𝑥+3𝑦=6 𝑦=−2𝑥+3 𝑦−10=−3𝑥

Homework (3/15/2017) Worksheet: Lesson 5.1-5.3 Review

Homework 3/16/2017 Worksheet: Lesson 5.4_#1-10 3/17/2017 Worksheet: Lesson 5.4_#11-20

Homework (3/20/17) Worksheet: Systems of Equations Word Problems

Methods of Solving Systems of Linear Equations Graphing  both equations need to be in SLOPE-INTERCEPT FORM Example: 𝑦=4𝑥+1 𝑎𝑛𝑑 𝑦=− 1 3 𝑥+3 Substitution both equations can be in any form Example: 2𝑦=4𝑥−4 𝑎𝑛𝑑 4𝑥+6𝑦=6 Example: 𝑥=3𝑦+1 𝑎𝑛𝑑 𝑥=4 Example: 𝑦=3𝑥 𝑎𝑛𝑑 3𝑥−5𝑦=2 Elimination  both equations need to be in STANDARD FORM Example: 3𝑥−6𝑦=12 𝑎𝑛𝑑 −3𝑥+2𝑦=1

Numbers of Solutions No Solutions Graph: parallel lines Solving the equations: when both sides are not equal to each other. Ex. 6≠4

Numbers of Solutions One Solution Graph: intersecting lines Solving the equations: when you have an answer. Ex. y = 3 and x = 1 (1,3)

Numbers of Solutions Infinite Many Solutions Graph: it is the same line, so one line is on top of the other line Solving the equations: when both sides are equal to each other. Ex. 3=3