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Published byJulius Thornton Modified over 6 years ago

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Chapter 7 – Solving Systems of Linear Equations 7.3 – Solving Linear Systems by Linear Combinations

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Today we will be learning how to: Use linear combinations to solve a system of linear equations Model a real-life problem using a system of linear equations

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7.3 – Solving Linear Systems by Linear Combinations Example 1 Solve the linear system. -x + 2y = -8 x + 6y = -16

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7.3 – Solving Linear Systems by Linear Combinations A linear combination of two equations is an equation obtained by adding one of the equations (or a multiple of that equation) to the other equation (or a multiple of that equation).

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7.3 – Solving Linear Systems by Linear Combinations Example 2 Solve the linear system. 5x – 4y =3 2x + 8y = -2

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7.3 – Solving Linear Systems by Linear Combinations Example 3 Solve the linear system. 3x = -6y + 12 -x + 3y = 6

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7.3 – Solving Linear Systems by Linear Combinations STEPS FOR SOLVING A LINEAR SYSTEM BY LINEAR COMBINATIONS 1. 2. 3. 4.

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7.3 – Solving Linear Systems by Linear Combinations Example 4 Solve the linear system. 11x + 3y = 1 -5x – 3y = -7

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7.3 – Solving Linear Systems by Linear Combinations Example 5 Solve the linear system. 2u = 4v + 8 3v = 5u – 13

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7.3 – Solving Linear Systems by Linear Combinations HOMEWORK Page 414 #8 – 24 even

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