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Simultaneous Equations by Substitution 15-Feb-14 Solving Using the Substitution Method © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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y x – 7 – 6 – 5 – 4 – 3 – 2 – x 1234 y 4567 x 1234 y 2468 Solve with a graph y = x + 3 y = 2x x = 3 y = 6 x = 3 y = 6 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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Solve, by substitution: y = x + 3 (1) y = 2x (2) Substitute the y in equation (1) with the 2x from equation (2) to obtain equation (3) 2x = x + 3 (3) 2x – x = 3 x = 3 Now put the value x = 3 into either of the two original equations to find the value of y y = x + 3 (1) y = y = 6 x = 3 y = 6 x = 3 y = 6 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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1. y = x y = 2x + 1 y = 2x y = 3x 2. y = 2x y = x + 5 y = 3x y = 2x – 3 3. y = x – 56. y = x – 7 y = 2x y = 3x – 11 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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1. y = x y = 2x + 1 y = 2x y = 3x x = 4 and y = 8x = 1 and y = 3 2. y = 2x y = x + 5 y = 3x y = 2x – 3 x = 7 and y = 21x = 8 and y = y = x – 56. y = x – 7 y = 2x y = 3x – 11 x = -5 and y = -10x = 2 and y = -5 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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

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1. y = x 2 + 8x y = x 2 – 4x – 7 y = x y = 3 – x 2. y = x 2 + 8x y = x 2 – 5x – 35 y = 3x y = 2x – 5 3.y = x 2 – 5x – 56. y = x 2 + x y = 1 – 4x y = x © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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1. y = x 2 + 8x y = x 2 – 4x – 7 y = x y = 3 – x x = -3 and -4x = -2 and 5 2. y = x 2 + 8x y = x 2 – 5x – 35 y = 3x y = 2x – 5 x = -2 and -5x = -3 and 10 3.y = x 2 – 5x – 56. y = x 2 + x y = 1 – 4x y = x + 25 x = -2 and 3x = -5 and 5 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09

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