Name: Equations Reducible to a Pair of Linear Equations
Uploaded: 2019-07-19
Duration: 4 min 9 s
Description: Some equations may be in a form that can be reduced to a linear equation through substitution. Do you want to explore how this can be done? Watch the video t...

Question

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?) Represent this situation algebraically and graphically.

Accepted Answer

Let the present age of Aftab be $x$ and present age of daughter be $y$ .

Hence, seven years ago $,$ the age of Aftab $= x - 7$ and the age of the daughter $= y - 7$

Hence, as per the given condition, $(x - 7) = 7 (y - 7)$

$⟹ x - 7 = 7 y - 49$

$⟹ x - 7 y = - 42$ ……………(i)

Three years later, the age of Aftab $= x + 3$ and the age of the daughter $= y + 3$

Hence, as per the given condition, $(x + 3) = 3 (y + 3)$

$\Rightarrow x + 3 = 3 y + 9$

$\Rightarrow x - 3 y = 6$ ……………(ii)

Hence, equation (i) and (ii) represent given conditions algebraically as $x - 7 y = - 42$ and $x - 3 y = 6$

Graphical Representation:

$x - 7 y = - 42$

$\Rightarrow x = - 42 + 7 y$

Two solutions of this equation are:

$x$ $- 7$ $0$

$y$ $5$ $6$

$x - 3 y = 6$

$\Rightarrow x = 6 + 3 y$

Two solutions of this equation are

$x$ $6$ $0$

$y$ $0$ $- 2$

The graphical representation is as follows:

Exercise 3.1

Jharkhand Board Mathematics Solutions for Exercise 3.1

Questions from Exercise 3.1 with Hints & Solutions

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