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Solving Linear Systems Algebra II Solving Linear Systems

We will focus on 1 and 2 today. Main ways of solving Substitution Elimination Graphing We will focus on 1 and 2 today.

First Method: Substitution 1) Pick an equation and isolate a variable. 2) Plug value from step 1 into the second equation. Solve. 3) Plug value of the variable from step 2 into any equation. Solve. 4) Final answers is a coordinate: (x, y)

Substitution Example 1.) x + 2y = 6 3x – 2y = 2

Substitution Examples 2.) 4x + y = 7 3.) x + 3y = 3 2x + 5y = -1 2x – 4y = 6

Substitution Examples 4.) 2x – 3y = 3 5.) 2x – 5y = 9 -2x + y = -4 -3x + y = -7

Second Method: Elimination 1) Change equation(s) so that you have opposite coefficients for one of the variables. 2) Add equations straight down. Solve. 3) Take value of the variable from step 2 and plug into any equation. Solve. 4) Final answer is the coordinate (x, y).

Solve the system using elimination 1.) x – y = 7 2x + y = 5

Solve the system using elimination 2.) x + 2y = -11 3x – 2y = -1

Solve the system using elimination 3.) 3x – y = 4 2x + 3y = 32

Solve the system using elimination 4.) 2x + 5y = 0 4x + 6y = 24

Solve the system using elimination 5.) 3x – 4y = -4 -5x + 2y = 2

Homework Systems of Linear Equations Worksheet # 5-8, 15-18