Quit Introduction Substitution Operations Solving Equations Quit Our

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Introduction Substitution Operations Solving Equations Quit

• Our number system – the decimal system – uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to make all our numbers. • The Romans used the letters I, V, X, L, C, D, M to represent their numbers. • The Greeks used l a vertical bar for 1 Π Pi. . . . for 5 Δ Delta. . . for 10 H Eta. . . for 100 X Chi. . . for 1000 M Mu. . . for 10, 000 Quit

• These symbols and letters are the numbers in these systems. • Algebra is different. • Algebra is about using a letter for an unknown number. • A letter, usually x or y, is substituted instead of a number. Quit

You are in a shop. A sign says 6 apples for 90 cent. You can probably work out in your head how much one apple costs. But if we want to use maths to find the cost, we use algebra. We let x = cost of one apple. 6 apples costs 90 cent ⇒ 6 multiplied by (cost of one apple) = 90 cent ⇒ 6 multiplied by x = 90 ⇒ 6 x = 90 Quit 90 or divide by 6: x = –– = 15 cent each 6

Sign in window of Sally’s fruit shop: 8 apples for € 1 Sign in window of Herb’s fruit shop: 6 apples for 72 cent. Which shop is cheaper for apples? Sally’s shop Herb’s shop 8 x = 100 6 x = 72 100 x = ––– = 12· 5 cent each 8 72 x = ––– = 12 cent each 6 Herb is cheaper Quit

Substitution a = 3, b = 3, find the value for: • a+b =2+3=5 • 2 a + b = 2(2) + 3 = 4 + 3 = 7 • a 2 + b = 22 + 3 = 4 + 3 = 7 • 3(a + b) = 3(2 + 3) = 3(5) = 15 • 4 a 2 + 2 b = 4(2)2 + 2(3) = 4(4) + 2(3) = 16 + 6 = 22 Quit

Multiplication • • • Quit a a = a 2 c c c = c 3 3 a 2 a = 6 a 2 5 a = 5 a a b = ab

Addition and Subtraction • • • Quit a + 4 a = 5 a 2 a + 3 b = 5 a + 3 b 3 a + 5 a + 4 a 2 + 2 a 2 + b = 8 a + 6 a 2 + b 4 c 2 + 3 c + c = 4 c 2 + 4 c a + b + a 2 + b 2 + 2 a + 3 b = 3 a + 4 b + a 2 + b 2

Simplification • • • Quit 4 a + 6 c = 2(2 a + 3 c) 10 a + 2 b = 2(5 a + b) 10 a + 20 b + 5 c = 5(2 a + 4 b + c) 15 a – 3 b = 3(5 a – b) 4 a + 8 a 2 = 4 a(1 + 2 a)

Solving Equations 3 x + y = 13 2 x – 2 y = – 5 + 6 x + 2 y = 26 ______ = 21 Divide both sides by 7 7 x x=3 Quit 3(3) + y = 13 Substitute into equation 9 + y = 13 y=4

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