Question

Obtain a pair of linear equations in two variables from the
following information

Father tells his son, Five years ago, I was seven times as old as you were. After five years,I will be three times as old as you will be.

Answer 1

Let age of father ${=}^{\prime }{x}^{\prime }$ years (present)

Let age of son ${=}^{\prime }{y}^{\prime }$ years (present)

$x-5=7(y-5)$

$\therefore 7y-x=30$ ……….$\left(1\right)$

$x+5=3(y+5)$

$x-3y=10$ ……….$\left(2\right)$

Pair of equations are $x-3y=10$ and $7y-x=30$

Adding $\left(1\right)$ and $\left(2\right)$

$4y=40$ $\Rightarrow y=10$

$\therefore$ $x-30=10$

$x=40$

$\therefore x=40$ and $y=10$.