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Alg II 3-2 Solving Systems Algebraically

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Alg II 3-2 Solving Systems Algebraically

1. 1. 3-2 Solving SystemsAlgebraicallyAlgebra II Unit 3 Linear Systems© Tentinger
2. 2. Essential Understanding andObjectives• Essential Understanding: you can solve a system of equations by writing equivalent systems until the value of one variable is clear. Then substitute to find the values of the other variable• Objectives:• Students will be able to solve linear systems algebraically
3. 3. Iowa Core Curriculum• Algebra• A. CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.• A.CED.3 . Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.• A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.• A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
4. 4. Substitution Method• Use this method to solve a system of equations when it is easy to isolate one of the variables.• After isolating one of the variables, substitute for that variable in the other equation.• Then solve for the other variable
5. 5. Example• What is the solution to the system of equations? ì3x + 4y = 12 í î2x + y = 10• Step 1: solve the equation for one of the variables• Step 2: Substitute the expression for y in the other equation. Then solve for x• Step 3: Substitute the value for x into one of the original equations. Solve for y.
6. 6. Example• What is the solution of the system of equations? ì x + 3y = 5 í î-2x - 4y = -5