At the present time a man is four times as old as his son. Six years ago he was 10 times as old. Find their present ages.

Son = x

Man = 4x

Son = (x - 6)

Man = (4x - 6)

And, we have also been given a relation between the age of son and man six years ago, that is, six years ago, the age of man was 10 times that of the age of son. Using that relation, we can set up an equation as follows:

(4x - 6) = 10(x - 6)

→ 4x - 6 = 10x - 60

→ 10x - 4x = 60 - 6

→ 6x = 54

→ x = 9

And we have assumed that present age of Son is x years and that of man is 4x years. Hence:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

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