Mr. Hartzer, Hamtramck High School 2017-18 Algebra II Mr. Hartzer, Hamtramck High School 2017-18

DO NOW

DO NOW (Honors)

This Week’s Objective Students will: solve linear equations and inequalities using graphs and algebraic methods.

Today’s Objective Students will: use substitution and elimination to solve linear systems exactly. CCSS: A-REI.C.6; A-REI.C.5; A-CED.A.2

Today’s Agenda Do Now Review homework Notes: Algebraic Techniques Practice

Solving by Elimination To solve by elimination: (1) Multiply one or both equations to create matching coefficients. (2) Take the difference of the equations to eliminate one variable. (3) Solve for the value of the other variable. (4) Use this value in either equation to solve for the value of the first variable.

Solving by Elimination Example: 3𝑥+4𝑦=12 2𝑥+𝑦=10 (1) Multiply one or both equations to create matching coefficients. 4 2𝑥+𝑦=10 ⇒ 8𝑥+4𝑦=40

Solving by Elimination Example: (2) Take the difference of the equations to eliminate one variable. 8𝑥+4𝑦=40 3𝑥+4𝑦=12 5𝑥=28

Solving by Elimination Example: (3) Solve for the value of the variable. 5𝑥=28 𝑥=5.6

Solving by Elimination Example: (4) Use this value in either equation to solve for the value of the first variable. 2𝑥+𝑦=10 2 5.6 +𝑦=10 𝑦=−1.2

Solving by Elimination Example: 3𝑥+4𝑦=12 2𝑥+𝑦=10 Solution: Both lines pass through (5.6, −1.2)

Solving by Elimination 1. 2. 3. 4. Solution:

Solving by Elimination 1. 2. 3. 4. Solution:

Solving by Elimination 1. 2. 3. 4. Solution:

Classwork Complete the worksheet. Work with your neighbor.