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Simultaneous Equations elimination

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What are they? Simply 2 equations –With 2 unknowns –Usually x and y To SOLVE the equations means we find values of x and y that –Satisfy BOTH equations [work in] –At same time [simultaneously]

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Elimination Method 2x – y = 1 3x + y = 9 We have the same number of ys in each If we ADD the equations, the ys disappear + 5x = 10 Divide both sides by 5 x = 2 A B Substitute x = 2 in equation A 2 x 2 – y = 1 4 – y = 1 y = 3 Answer x = 2, y = 3

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Elimination Method 5x + y = 17 3x + y = 11 We have the same number of ys in each If we SUBTRACT the equations, the ys disappear - 2x = 6 Divide both sides by 2 x = 3 A B Substitute x = 3 in equation A 5 x 3 + y = y = 17 y = 2 Answer x = 3, y = 2

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Elimination Method 2x + 3y = 9 2x + y = 7 We have the same number of xs in each If we SUBTRACT the equations, the xs disappear - 2y = 2 Divide both sides by 2 y = 1 A B Substitute y = 1 in equation A 2x + 3 = 9 2x = 6 x = 3 Answer x = 3, y = 1

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Elimination Method 4x - 3y = 14 2x + 3y = 16 We have the same number of ys in each If we ADD the equations, the ys disappear + 6x = 30 Divide both sides by 6 x= 5 A B Substitute x = 5 in equation A 20 – 3y = 14 3y = 6 y = 2 Answer x = 5, y = 2

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Basic steps Look at equations Same number of xs or ys? If the sign is different, ADD the equations otherwise subtract tem Then have ONE equation Solve this Substitute answer to get the other CHECK by substitution of BOTH answers

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What if NOT same number of xs or ys? 5x + 2y = 17 3x + y = 10 - x = 3 In B A B 5 x 3 + 2y = y = 17 y = 1 Answer x = 3, y = 1 If we multiply A by 2 we get 2y in each 5x + 2y = 17 6x + 2y = 20 B A

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What if NOT same number of xs or ys? 3x + 6y = 21 4x - 2y = x= 45 In B A B 3 x 3 + 6y = 21 6y = 12 y = 2 Answer x = 3, y = 2 If we multiply A by 3 we get 6y in each 3x + 6y = 21 12x - 6y = 24 B A x = 3

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…if multiplying 1 equation doesnt help? 3x + 7y = 26 5x + 2y = y = 58 In B A B 5x + 2 x 2 = 24 5x = 20 x = 4 Answer x = 4, y = 2 Multiply A by 5 & B by 3, we get 15x in each 15x + 35y = x + 6y = 72B A y = 2 Could multiply A by 2 & B by 7 to get 14y in each

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…if multiplying 1 equation doesnt help? 3x - 2y = 7 5x + 3y = x = 95 In B A B 5 x 5 + 3y = 37 3y = 12 y = 4 Answer x = 5, y = 4 Multiply A by 3 & B by 2, we get +6y & -6y 9x – 6y = 21 10x + 6y = 74B A x = 5 Could multiply A by 5 & B by 3 to get 15x in each

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Independent Practice Solve #2 a, b, c #4 d, e, f,g

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