A father is now two times as old as his son. Sixteen years ago he was 6 times as old as his son. How old are the father and son now?

40 years and 20 years

Step-by-step explanation:

Let the father's age be y and son's age x

Father is currently twice son's age i.e 2x

16 years ago, the son was (x-16) years old

the father was (y-16) or (2x-16) years old(i)

The second sentence states that the father was 6 times his sons age 16 years ago i.e 6(x-16)yrs old(ii)

Equating (i) to (II) gives 2x-16 = 6(x-16)

2x-16 = 6x-96

Collecting like terms, 96-16 = 6x-2x, 80 = 4x, x = 20

Therefore, son's age is 20years and fathers age is twice son's age = 40 years

{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

do you have a picture of the table