Question

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".Obtain a pair of linear equation in two variables from the given information.

Answer 1

HELLO DEAR,

let the present age of father be x year.
and the present of son be y years.

according to questions,

Before 5 years
age of father = (x - 5)years
age of son = (y - 5)years

but Five years ago, I was seven times as old as you were:

x - 5 = 7(y - 5)

x - 5 = 7y - 35

x - 7y = -30

x - 7y = 30----------( 1 )


Now,

after 5 years,
age of father = (x + 5)years
age of son = (y + 5)years

but After five years, father will be three times as old as you will be".

so, (x + 5) = 3(y + 5)

x + 5 = 3y + 15

x - 3y = 10

x - 3y - 10 = 0----------( 2 )

hence, the required equation are given,


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Dear Student,

Solution:

let the present age of Father is x years

and present age of son is y years.

Now,as 5 years ago

age of Father was (x-5) years and so as his son was (y-5) years old.

after 5 years both ages are (x+5) and (y+5) years.

A.T.Q
Five years ago,Father was seven times as old as his son were

So,
$(x - 5) = 7(y - 5) \\ \\ x - 7y - 5 + 35 = 0 \\ \\ x - 7y + 30 = 0$
After five years, Father will be three times as old as his son will be.

$(x + 5) = 3(y + 5) \\ \\ x - 3y + 5 - 15 = 0 \\ \\ x - 3y - 10 = 0$
Thus by this way these are the two equations which represents the above situation in pair of two linear equation.

Hope it helps you.