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**Solving Using the Substitution Method**

Simultaneous Equations by Substitution 28-Mar-17 Solving Using the Substitution Method © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**y x x = 3 y = 6 Solve with a graph y = x + 3 y = 2x x y x y 1 2 3 4 5**

7 y x 1 2 3 4 5 6 7 8 –7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 x 1 2 3 4 y 6 8 x = 3 y = 6 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**Now put the value x = 3 into either of the two original equations to find the value of y**

y = x + 3 (1) y = 3 + 3 y = 6 Solve, by substitution: y = x (1) y = 2x (2) Substitute the y in equation (1) with the 2x from equation (2) to obtain equation (3) 2x = x (3) 2x – x = 3 x = 3 x = 3 y = 6 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x 2. y = 2x + 7 5. y = x + 5**

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x x = 4 and y = 8**

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**Choose the pair with a sum of 5**

y = x2 + 2x – 8 y = 6 – 3x 1 x –14 = -14 2 x – 7 = -14 7 x – 2 = -14 14 x –1 = -14 Choose the pair with a sum of 5 = 5 7 – 2 = 5 6 – 3x = x2 + 2x – 8 0 = x2 + 2x + 3x – 8 – 6 0 = x2 + 5x – 14 0 = (x + 7)(x – 2) x = -7 and +2 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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1. y = x2 + 8x + 12 y = x2 – 4x – 7 y = x y = 3 – x 2. y = x2 + 8x + 10 y = x2 – 5x – 35 y = 3x y = 2x – 5 y = x2 – 5x – 5 6. y = x2 + x y = 1 – 4x y = x2 + 25 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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**1. y = x2 + 8x + 12 y = x2 – 4x – 7 y = x y = 3 – x x = -3 and -4**

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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