Seven years ago, my mother was seven times older than me.
In exactly eight years from now, my mother will be two times older than me.
How old is my mother now?
Let x = mom's age (now)
Then y = my age (now)
Seven years ago: (x - 7) = 7(y - 7) ---> x - 7 = 7y - 49 ---> x - 7y = -42
Eight years from now: (x + 8) = 2(y + 8) ---> x + 8 = 2y + 16 ---> x - 2y = 8
Combining: x - 7y = -42 ---> x - 7y = -42
x - 2y = 8 ---> multiply by -1 ---> -x + 2y = -8
Adding down the columns: -5y = -50
Dividing: ---> y = 10 (my age now)
Substituting: x - 2y = 8 ---> x - 2(10) = 8 ---> x = 28 (mom's age now)