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**Ch 5.3 Elimination (addition)**

Objective: To solve a system of linear equations using elimination with addition.

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**Review Graphic Method Substitution Method - Time consuming**

If b = a and b = c solution then a = c. - Time consuming - Not always convenient - Not always accurate

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**Definition Rules Check Your Answers! Eliminate: Get rid of**

Rearrange the equations so that “like” terms are lined up. Add (or subtract) the two equations to each other to eliminate a variable. 3) Solve for the remaining variable. 4) Plug in your solution into either of the equations 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 p + 4q = 23 -p + q = 2 + -p + q = 2 -p +( ) = 2 5 5q = 25 -p = -3 q = 5 (-1) (-1) p = 3 p = 3, q = 5

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**Solve using elimination**

Example 2 Solve using elimination x + 3y = 3 x + 6y = 3 - x + 3y = 3 ( ) x + 3( ) = 3 -3y = 0 y = 0 x = 3 x = 3, y = 0

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**Solve using elimination**

Example 3 Solve using elimination t + r = 1 2r - t = 2 t + r = 1 -t + 2r = 2 + 3r = 3 t + r = 1 t + ( ) = 1 1 r = 1 t = 0 r = 1, t = 0

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**Solve using elimination**

Example 4 Solve using elimination 2x + y = 6 3x - y = 4 + 2x + y = 6 5x = 10 2( ) + y = 6 2 4 x = 2 y = 2 x = 2, y = 2

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**Solve using elimination**

Example 5 Solve using elimination x + 3y = 5 -x + y = 3 + x + 3y = 5 4y = 8 x + 3( ) = 5 2 6 y = 2 x = -1 x = -1, y = 2

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**Classwork 7x + 4y = -16 9x – 7y = -4 -7x – 6y = -4 -9x + y = 16**

1) 7x + 4y = -16 2) 9x – 7y = -4 -7x – 6y = -4 -9x + y = 16 3) 7x – 8y = 14 4) -3x + 6y = -6 7x – 9y = 7 -8x + 6y = 4

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**6x + 3y = -15 2x – 6y = 24 2x + 3y = -11 -3x - 6y = 24 -x + 2y = 6**

5) 6x + 3y = -15 6) 2x – 6y = 24 2x + 3y = -11 -3x - 6y = 24 7) -x + 2y = 6 8) -4x + 3y = 21 x + 8y = -26 -4x + 4y = 24

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