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Published byHilda Lawrence Modified over 8 years ago

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**6.2 Solve a System by Using Linear Combinations**

Secondary One 6.2 Solve a System by Using Linear Combinations

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Linear Combination AKA – Elimination: Obtained by adding one of the equations (or a multiple of one of the equations) to the other equation.

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**How to solve a system by using Linear Combination**

1. arrange the equations in standard form 2. make sure one of the variables contains an opposite coefficient. If not, make one opposites but multiplying one or both equations. 3. Add the equations vertically combining like terms 4. Solve for remaining variable 5. Substitute solution in step 4 into either equation and solve for remaining variable 6. Check solution by plugging it in.

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**Solve by Linear Combination**

4x + 3y = 16 2x – 3y = 8

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**Solve by Linear Combination**

-x + 2y = -8 x + 6y = -16

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**Solve by Linear Combination**

8x – 4y = -4 4y = 3x + 14

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**Solve by Linear Combination**

4x + 3y = 2 5x + 3y = -2

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**Solve by Linear Combination**

3x + y = 24 7x – 3y = 8

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**Solve by Linear Combination**

x + y = 1 5x + 4y = 14

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**Solve by Linear Combination**

y + 3x = 2 2y + 6x = 10

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**Solve by Linear Combination**

2y + 3x = 7 4y + 6x = 14

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**Solve by Linear Combination**

-3x – 4y = 27 5x – 6y = -7

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Assignment 6.2 Assignment

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