Example 5 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Example 5 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.” (Isn’t this interesting?) Solve by the method of substitution.. Let the Current age of Aftab be x years. & let Current age of Aftab’s daughter be y years. Given that “Seven years ago, I was seven times as old as you were then” Seven years ago, Age of Aftab = x − 7 Age of Aftab’s daughter = y − 7 Aftab was seven times as old as Aftab’s daughter (x – 7) = 7(y – 7) (x – 7) = 7y – 49 x – 7y = 7 − 49 x – 7y = −42 Also, “three years from now, I shall be three times as old as you will be “ 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 – 3y = 9 − 3 x – 3y = 6 So, our equations are x – 7y = −42 ...(1) x – 3y = 6 …(2) From (1) x – 7y = −42 x = 7y – 42 Putting value of x in (2) x – 3y = 6 (7y – 42) – 3y = 6 7y − 3y = 6 + 42 4y = 48 y = 48/4 y = 12 Putting y = 12 in equation (1) x – 7y = −42 x – 7(12) = −42 x − 84 = −42 x = −42 + 84 x = 42 So, x = 42, y = 12 is the solution of the equations Hence, Aftab’s age = x = 42 years His daughter’s age = y = 12 years