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**6.3 – Solving Systems of Linear Equations by Elimination.**

Definitions of the Day (DODs) Review of Ch 6 Systems of Equations So Far… 6.1 Graphing 6.2 Substitution Method 6.3 Elimination Method

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Definition: Elimination Method –Eliminate one of the variables by adding (or subtracting) the equations of the system. Let us Explore… x y 10 + = Top Equation + x ( - y = ) + 36 Bottom Equation 2x = 46 Y has been ELIMINATED x 23 , y =-13 = Solve for x, Substitute for y

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**Steps to the Elimination Method!!**

Pick One Variable to Eliminate! (Either x or y.) 2. Eliminate the Variable by adding or subtracting the equations together. 3. Substitute & Solve for the last Variable.

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Example #1 5x - 6y = -32 3x + 6y = 48

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Example #2 X+Y=6 X+3Y=10

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WARNING! WE MAY NEED TO MANIPULATE ONE OF THE EQUATIONS BEFORE SOLVING FOR A VARIABLE!

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**Example #3 (One Solution)**

3x + 4y = -10 5x - 2y = 18

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**Example #4 (No Solution)**

2x - 3y = 6 6x - 9y = 9

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**Example #5 (Infinitely Many Solutions)**

x + 4y = 1 3x + 12y = 3

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**Your Turn!! Solve by ELIMINATION 1. X+ y = 12 2. 4x - 2y = 6**

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Sentence Frames The Goal of Solving a System of Equations by Elimination is __________________________________________________________________________________________________ The Three methods for solving a System of Equations are 1. _______________ 2. _______________ 3. _______________

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