Question

if 5/x-1+1/y-2=2 and 6/x-1 -3/y-2=1

Answer 1

Solution:-

5/x-1 + 1/y-2 = 2
6/x-1 - 3/y-2 = 1

Let 1/x-1 = a and 1/y-2 = b, then,
5a + b = 2 (i)
6a - 3b = 1 (ii)

If we multiply equation (i) by 3, we get,
15a + 3b = 6 (iii)

Now, by adding equation (ii) and (iii), we get,
21a = 7
a = 1/3

If we put this value in equation (ii), we get,
6×1/3 - 3b =1
2-3b = 1
-3b = 1-2
-3b = -1
b = 1/3

Then,
a = 1/x-1 = 1/3

1/x-1 = 1/3
3 = x - 1
x = 4 Ans.

&

b = 1/y-2 = 1/3

1/y-2 = 1/3
3 = y-2
y = 5 Ans.

Ans.) The value of x is 4 and y is 5.