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**Solving Linear Equations**

Elimination S. Calahan

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**x + 2y = 5 -x + y = 13 Example Eliminate the x since the**

co-efficients are opposites.

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x + 2y = 5 -x + y = 13 3y = 18

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3y = 18 y = 6

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**Use one of the original equations to substitute y =6. x + 2y = 5 **

y = 6, so find x Use one of the original equations to substitute y =6. x + 2y = 5 x + 2(6) = 5 x + 12 = 5

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x + 12 = 5 x + 12 = 5 Solve = -12 x = - 7 Since y = 6 and x = -7, then the solution is (-7, 6)

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**Solve the system of equations.**

2x – 6y = 6 2x + 3y = 24 Notice the x co-efficients are the same.

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**Subtract the equations 2x – 6y = 6 - (2x + 3y = 24)**

Distribute the negative

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Now add 2x – 6y = 6 -2x - 3y = -24 -9y = - 18 y = 2

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**Using one of the 2 equations solve for x**

2x – 6y = 6 Remember y = 2 So, 2x – 6(2) = 6 2x – 12 = 6 2x = 18

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2x – 12 = 6 2x = 18 x = 9

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So the solution is (9, 2)

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