Question

If 7/x+8/y=2 , 2/x+12/y =20 then x=

Answer 1

$\boxed{\sf{x = \frac{ - 1}{2} }}$

Given:-

7/x + 8/y = 2

2/x + 12/y = 20

To find:-

The value of x.

Solution:-

Let 1/x = a and 1/y = b

then,

7a + 8b = 2 -------eq. 1.

2a + 12b = 20 -------eq. 2.

By using the method of elimination,

Multiply eq. 1 by 2 and eq. 2 by 7.

14a + 16b = 4

14a + 84b = 140

Now subtract equation 1. and 2.

We get,

14a +16b = 4

- 14a - 84b = -140

_____________________

-68b = - 136

cancelling out the negative sign,

68b = 136

b = 136 / 68

b = 2

Now,put the value of 2 in equation 1.

7a + 8*2 = 2

7a +16 = 2

7a = 2 - 16

7a = -14

a = -2

We have, a = 1/x

-2 = 1/x

-2x = 1

x = -1/2