NEED HELP IN ALGEBRA PLEASE SOLVE THIS DIGIT WORD PROBLEMS!

Please solve this problem and please explain to me clearly how did you do it so I can learn how to solve this things..

PROBLEM
The sum of the reciprocals of 2 numbers is 9. Twice the reciprocal of the first is 12 less than 4 times the reciprocal of the 2nd. Find the numbers.

Hello,

You just need to learn to read:

►First sentence
"2 numbers" ↔ x and y
"the reciprocals of 2 numbers" ↔ 1/x and 1/y
"The sum of the reciprocals of 2 numbers" ↔ 1/x + 1/y
"The sum of the reciprocals of 2 numbers is 9." ↔ 1/x + 1/y = 9

►Second sentence:
"the first" ↔ x
"the reciprocal of the first" ↔ 1/x
"Twice the reciprocal of the first" ↔ 2 × 1/x
"the 2nd" ↔ y
"the reciprocal of the 2nd." ↔ 1/y
"4 times the reciprocal of the 2nd." ↔ 4 × 1/y
"Twice the reciprocal of the first is 12 less than 4 times the reciprocal of the 2nd."↔ 2 × 1/x + 12 = 4 × 1/y

►Hence you get the equations:
  { 1/x + 1/y = 9
  { 2/x + 12 = 4/y

Let's have X=1/x and Y=1/Y to simplify the equations:
  { X + Y = 9
  { 2X + 12 = 4Y

The second equation can be divided by 2:
  { X + Y = 9
  { X + 6 = 2Y

Subtract second equation from first one:
(X - X) + (Y - 6) = (9 - 2Y)
3Y = 15
Y = 5

Then X = 9 - Y = 4
And x=1/X = ¼
And y = 1/Y = 1/5

►So the final answer is:
The first value is ¼ and the second value is 1/5.

Explicatively,
Dragon.Jade :-)

hi, here is the answer.
let the 2 no.s be x and y
now sum of the reciprocals is 9: 1/x + 1/y = 9
which simplifies to: x = y / (9y-1)
then 2nd statement: 4(1/y) - 12 = 2(1/x)
which simplifies to: x=2y / (4-12y)
on equating: y / (9y-1) = 2y / (4-12y)