### Chapter 3: Pair of Linear Equations in Two Variables

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##### Pair of linear equations in two variables CBSE NCERT Solutions

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.

Solution: Let the present age of Aftab and his daughter be x years and y years respectively.

Seven years ago, the age of Aftab is (x-7) years and the age of his daughter is (y-7) years.
According to the given condition,

$(x-7) = 7(y-7)$

$\Rightarrow x - 7 = 7y - 49$

$\Rightarrow x - 7y = 7 - 49$

$\Rightarrow x - 7y = - 42$

Thus, these given conditions can be algebraically represented as x - 7y = - 42  .

Again, Three years hence, the age of Aftab will be (x + 3) and the age of his daughter will be (y + 3).
According to the given condition,

(x + 3) = 3(y + 3)

$\Rightarrow$ x + 3 = 3y + 9

$\Rightarrow$ x - 3y = 6

Thus, this given conditions can be algebraically represented as x - 3y   = 6.

Three solutions of equation x = – 42 + 7y can be written in a table as follows:

 x -7 0 7 y 5 6 7

Three solutions of equation x = 6 + 3y can be written in a table as follows:

 x 6 3 0 y 0 -1 -2

The graphical representation is as follows:

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