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Solving Equations Learning Outcomes Manipulate and simplify simple expressions including removal of brackets Solve linear equations, with or without brackets Solve linear equations with fractions Use trial and improvement to solve equations Revise algebraic simultaneous equations

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a) 6x + 3 + 4x - 2 b) 3x - 4 + 2x - 7 c) 4x + 3y + 6 - 4x + 2y d) x 2 + 2x – 4 + x 2 - 3x - 5 e) 3xy + y 2 + x 2 – 2xy – 3y 2 f) 5x 3 + 3xy + 6x 2 - xy + 2x 3 Solving Equations Simplifying Expressions Simplify the following expressions

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e) (x + 1)(x + 2) f) (x - 3)(x + 4) g) (2x – 1) 2 a) 3(x + 4) b) 4(x + 1) – 3(x + 1) c) 5(x – 2) – 2(x – 4) d) x(x + 1) – 2(x + 1) Solving Equations Expanding Brackets Expand and simplify the expressions below

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Solving Equations Linear Equations Solve a)2x – 6 = 8 d) x + 2(x+1) = 4x b)7 – 3x = 14 e) 5(x-2) = 3(2x -4) c)-2x + 4 = 6x - 16

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Solving Equations with Fractions Solve 1) 2) 3)

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Solving Equations with Fractions Solve 4) 5)

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Solving Equations with Fractions Solve 6) 7)

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Solving Equations Trial and Improvement Solve to 1dp by trial & improvement a) x 2 + x = 20.7 xx 2 + x comment Solution lies between 4 & 6

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Solving Equations Trial and Improvement Solve to 1dp by trial & improvement b) xx(x + 1) comment In the rectangle ABCD has an area of 100cm 2. Side AB is 1cm longer than BC. Find the length of side BC. A B CD 100cm 2

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Solving Equations Solving Simultaneous Equations 1. 2x + y = 8 x + y = 5 2. 2x + y = 7 3x + 2y = 11 3. 7x - 3y = 20 2x + 4y = -4 Solve the following simultaneous equations

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Solving Equations Solving Quadratic Equations Solving equations involving x 2 terms (x + 3) 2 = (x – 1) 2 + 8 2

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Solving Equations Additional Notes

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Solving Equations Learning Outcomes: At the end of the topic I will be able to Manipulate and simplify simple expressions including removal of brackets Solve linear equations, with or without brackets Solve linear equations with fractions Use trial and improvement to solve equations Revise algebraic simultaneous equations Can Revise Do Further

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EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

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