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Systems of Equations: Elimination, Part II Unit 7, Lesson 5b

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Type #2: Multiply one equation to force a variable cancel Solve by elimination.3x + 6y = –6 –5x – 2y = –14 Step 1: Eliminate one variable. Add the equations to eliminate y. 3x + 6y = –6 –15x – 6y = –42 –12x – 0 = –48 To prepare to eliminate y, multiply the second equation by 3. 3x + 6y = –6 3(–5x – 2y = –14) Step 2: Solve for x. –12x = 48 x = 4

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Type #2: Multiply one equation to force a variable cancel Solve by elimination.3x + 6y = –6 –5x – 2y = –14 Step 3: Solve for the eliminated variable using either of the original equations. 3x + 6y = –6 3(4) + 6y = –6 12 + 6y = –6 6y = –18 y = –3 The solution is (4, –3).

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x + 2y = 11 –3x + y = –5 Solve the system by elimination. x + 2y = 11 –2(–3x + y = –5) x + 2y = 11 +(6x –2y = +10) 7x + 0 = 21 7x = 21 x = 3 Another Example: x + 2y = 11 3 + 2y = 11 –3 2y = 8 y = 4 (3, 4)(3, 4)

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Solve the system by elimination. 3x + 2y = 6 –x + y = –2 3x + 2y = 6 3(–x + y = –2) 3x + 2y = 6 +(–3x + 3y = –6) 0 + 5y = 0 5y = 0 y = 0 One More Example: –x + y = –2 –x + 3(0) = –2 –x + 0 = –2 –x = –2 (2, 0)(2, 0) x = 2

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Type #3:Multiply both equations by values that force a variable to cancel Solve by elimination.3x + 5y = 10 5x + 7y = 10 Step 1: Eliminate one variable. Subtract the equations to eliminate x. 15x + 25y = 50 15x + 21y = 30 0 + 4y = 20 To prepare to eliminate x, multiply one equation by 5 and the other equation by 3. 5(3x + 5y = 10) 3(5x + 7y = 10) Step 2: Solve for y. 4y = 20 y = 5

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Type #3:Multiply both equations by values that force a variable to cancel Solve by elimination.3x + 5y = 10 5x + 7y = 10 Step 3: Solve for the eliminated variable x using either of the original equations. 3x + 5y = 10 3x + 5(5) = 10 3x + 25 = 10 3x = –15 x = –5 The solution is (–5, 5).

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–5x + 2y = 32 2x + 3y = 10 Solve the system by elimination. 2(–5x + 2y = 32) 5(2x + 3y = 10) –10x + 4y = 64 +(10x + 15y = 50) 19y = 114 y = 6 Another Example: 2x + 3y = 10 2x + 3(6) = 10 –18 2x = –8 2x + 18 = 10 x = –4 (–4, 6)

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Solve the system by elimination. 2x + 5y = 26 –3x – 4y = –25 3(2x + 5y = 26) +(2)(–3x – 4y = –25) 6x + 15y = 78 +(–6x – 8y = –50) y = 4 0 + 7y = 28 One More Example: 2x + 5y = 26 2x + 5(4) = 26 (3, 4)(3, 4) x = 3 2x + 20 = 26 –20 2X = 6

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