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Ex 3.1, 1 - Aftab tells his daughter, Seven years ago - Ex 3.1

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
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Ex 3.1,1 Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically. Let the current age of Aftab be x years. & Let the current age of Aftab’s daughter be y years. Seven years ago, Age of Aftab = x − 7 Age of Aftab’s daughter = y − 5 Aftab was seven times as old as Aftab’s daughter (x – 7) = 7(y – 7 ) (x – 7) = 7y – 49 x – 7 – 7y + 49 = 0 x – 7y + 42 = 0 Three years later, Age of Aftab = x + 3 Age of Aftab’s daughter = y + 3 Aftab will be three times as Aftab’s daughter (x + 3) = 3(y + 3 ) (x + 3) = 3y + 9 x + 3 – 3y - 9 = 0 x – 3y − 6 = 0 Now, plotting equations x – 7y + 42 = 0 ...(1) x – 3y − 6 = 0 …(2) Solving (1) x – 7y + 42 = 0 7y = x + 42 y = (𝑥 + 42)/7 Solving equation (2) , x – 3y - 6 = 0 3y = x - 6 y = (𝑥 − 6)/3

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