Math, asked by ruturaj09, 10 months ago

^X/Y=4, 1/X+1/Y=1/XY convert into simultanious equation and solve

Answers

Answered by rawoolniraj062004

Answer:

x = 16/17

y = 1/17

Attachments:

Answered by Swarup1998

Simultaneous equations are

x - 16y = 0

x + y = 1

and the required solution is

x = 16/17, y = 1/17.

Step-by-step explanation:

The given equations are

√(x/y) = 4

or, x/y = 16

or, x = 16y

or, x - 16y = 0 ..... (1)

1/x + 1/y = 1/(xy)

or, (y + x)/(xy) = 1/(xy)

or, y + x = 1

or, x + y = 1 .... (2)

Thus we have the following simultaneous equations:

x - 16y = 0 ..... (1)

x + y = 1 ..... (2)

Now, we solve these equations.

1. Using 'substitution method'.

The equations to solve are

x - 16y = 0 ..... (1)

x + y = 1 ..... (2)

From (1), we get x = 16y

Now substituting x = 16y in (2), we get

16y + y = 1

or, 17y = 1

or, y = 1/17

Putting y = 1/17 in (1), we have

x - 16/17 = 0

or, x = 16/17

Therefore the required solution is

x = 16/17, y = 1/17

2. Using 'elimination method'.

The equations to solve are

x - 16y = 0 ..... (1)

x + y = 1 ..... (2)

Multiplying (1) by 1 and (2) by (1), we get

x - 16y = 0

x + y = 1

- - -

-------------------

- 17y = - 1

or, y = 1/17

Putting y = 1/17 in (1), we get

x - 16/17 = 0

or, x = 16/17

Therefore the required solution is