2. Example 1 Seven years ago A was seven times as old as B was then. Three years from now, A will be three times as old as B then. Represent this algebraically and find their present ages.
3. Equations Simplified x - 7y + 42 = 0 …..(1) x - 3y - 6 = 0 …..(2) Equations x – 7 = 7(y - 7) x + 3 = 3(y + 3)
4. Solution by Elimination x - 7y = - 42 …..(1) x - 3y = 6 …..(2) ---------------------------- (1) – (2): -4y = -48 y = 48/4 = 12 Substitute in (2): x – 36 = 6 x = 36 + 6 = 42 A’s present age = 42 B’s present age = 12
7. Example 3 Sania buys 3 bats and 6 balls for Rs 3900. Later she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and find the price of a bat and that of a ball.
9. Solution by elimination: 3x + 6y = 3900………………(1) x + 3y = 1300 ………………(2) ----------------- (1)…………………….. 3x + 6y = 3900…………..(3) (2)x3…………………. 3x + 9y = 3900……………(4) -------------------- (4)-(3)………………… 3y = 0 y = 0 x = 1300 What’s your conclusion? Try this using the Cross-Multiplication method.
10. Example 3 The cost of 2 kg of apples and 1 kg of grapes is Rs 160 and that of 3 kg of apples and 2 kg of grapes is Rs 300. Represent this situation algebraically and find the price per kg of apples and grapes.
