Form the pair of linear equations for the following problem and find their solution by the substitution method: 'Five years hence,the age of Jacob will be three times that of his son. Five years ago,Jacob's age was seven times that of his son. What are their present ages?'

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(N/A) Let the present age of Jacob be $x$ years and the present age of his son be $y$ years.
Case $1$: Five years hence,Jacob's age will be $(x + 5)$ and his son's age will be $(y + 5)$.
According to the problem,$(x + 5) = 3(y + 5) \implies x + 5 = 3y + 15 \implies x - 3y = 10$ (Equation $1$).
Case $2$: Five years ago,Jacob's age was $(x - 5)$ and his son's age was $(y - 5)$.
According to the problem,$(x - 5) = 7(y - 5) \implies x - 5 = 7y - 35 \implies x - 7y = -30$ (Equation $2$).
From Equation $1$,$x = 3y + 10$.
Substituting this value into Equation $2$: $(3y + 10) - 7y = -30 \implies -4y = -40 \implies y = 10$.
Substituting $y = 10$ into $x = 3y + 10$: $x = 3(10) + 10 = 40$.
Therefore,the present age of Jacob is $40$ years and the present age of his son is $10$ years.

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