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**Ch 5.4 Elimination (multiplication)**

Objective: To solve a system of linear equations using multi-step elimination (multiplication and addition).

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**Rules Check Your Answers!**

Rearrange the equations so that “like” terms are lined up. Multiply one of the equations so OPPOSITES exist for one of the variables. Add the two equations to each other to eliminate that variable. 4) Solve for the remaining variable. 5) Plug in the solution from Step 4 into either equation to solve for the other variable. Check Your Answers! Plug in the x and y solutions into BOTH equations to verify that they both make TRUE statements.

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**Solve using elimination**

Example 1 Solve using elimination -2( x + 6y = -3) 2x + 3y = 3 2x + 3y = 3 x + 6y = -3 Multiply by (-2) 2x + 3y = 3 -2x - 12y = 6 + -9y = 9 2x + 3y = 3 2x + 3(-1) = 3 y = -1 −3 +3 2x = 6 x = 3, y = -1 x = 3

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**Solve using elimination**

Example 2 Solve using elimination -2( x – 4y = 9) 2x + 3y = -4 2x + 3y = -4 x – 4y = 9 Multiply by (-2) -2x + 8y = -18 2x + 3y = - 4 + 11y = -22 2x + 3y = -4 2x + 3(-2) = -4 y = -2 −6 +6 2x = 2 x = 1, y = -2 x = 1

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**Solve using elimination**

Example 3 Solve using elimination -4x − y = -12 8x − 4y = 0 Multiply by (+2) 2(-4x – y = -12) 8x − 4y = 0 -8x − 2y = -24 + 8x − 4y = 0 -6y = -24 -4x − y = -12 -4x − (4) = -12 y = 4 -4x = -8 x = 2, y = 4 x = 2

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**Solve using elimination**

Example 4 Solve using elimination 2x +14y = -8 -6x + 7y = 24 Multiply by (+3) 3(2x + 14y = -8) -6x + 7y = 24 6x + 42y = -24 + -6x + 7y = 24 49y = 0 2x + 14y = -8 2x + 14(0) = -8 y = 0 2x = -8 x = -4, y = 0 x = -4

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Classwork 1) 4x + 5y = -22 2) -x + 2y = 20 2x + y = -26 5x + y = 10

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Classwork 3) -4x + 6y = 10 4) -2x – 5y = -16 -2x + 4y = 14 -x + y = 13

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Classwork 5) -4x + 3y = 15 6) 2x + 8y = -8 x – 6y = 12 -x − 10y = 16

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