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Published byDaisy McDaniel Modified over 7 years ago

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Solving Systems of Linear Equations By Elimination

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What is Elimination? To eliminate means to get rid of or remove. You solve equations by eliminating one of the variables (x or y) using addition and or subtraction.

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Example 1 Solve the following system of linear equations by elimination. 2x – 3y = 15 5x + 3y = 27 (1) (2) Add equation (1) to equation (2) 7x + 0y = 42 7x = 42 x = 6 By eliminating y, we can now solve for x

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Example 1 Substitute x= 6 into equation (1) to solve for y 2x – 3y = 15 2(6) – 3y = 15 12 – 3y = 15 – 3y = 15 – 12 – 3y = 3 y = -1 Check your solution x = 6 and y = -1 in equation (2) 5x + 3y = 27 5(6) + 3(-1) = 27 30 – 3 = 27 27 = 27 LS = RS Therefore, the solution set = {(6,-1)}

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Example 2 5x + 4y = -28 3x + 10y = -13 (1) (2) If we were to add these equations we would obtain 8x + 14y = -41 Even though we have only one equation now, we still have 2 variables. We need to multiply the equations by terms that will allow us to eliminate either x or y.

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Example 2 If we multiply equation (1) by 5 and equation (2) by -2, we be able to eliminate y. (1) x 5 (2) x -2 25x + 20y = -140 -6x – 20y = 26 (3) (4) When you change the equations you need to renumber them. 19x = -114 Add (3) & (4) x = -6 5x + 4y = -28 3x + 10y = -13 (1) (2)

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Example 2 Substitute x = -6 into equation (1) 5x + 4y = -28 5(-6) + 4y = -28 -30 + 4y = -28 4y = -28 +30 4y = 2 Check your answer x = -6 and y = ½ into equation (2) 3(-6) + 10(½) = -13 -18 + 5 = -13 -13 = -13 LS = RS Therefore, the solution set = {(-6, ½)}

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Questions? Any Questions? Homework: 1.4 # 5 – 12 Complete Homework for Monday! Have a Great Weekend

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