Question

(5/ x-1)+(1/y-2)=2,(6/x-1)-(3/y-2) then the value of x​

Answer 1

Answer:

First equation:

x−1

5

+

y−2

1

=2

or,

(x−1)(y−2)

5(y−2)+x−1

=2

xy−2x−y+2

5y−10+x−1

=2

= x+5y−11=2xy−4x−2y+4

or ,x+5y−11+4x+2y−4=2xy

or, 5x+7y−15=2xy

second equation:

x−1

6

−

y−2

3

=1

xy−2x−y+2

6y−12−3x+3

=1

= 6y−3x−9=xy−2x−y+2

6y−3x−9+2x+y−2=xy

or, 7y−x−11=xy

Multiply the second equation by 2 and subtract first equation from resultant

14y−2x−22=2xy

7y+5x−15=2xy

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

7y−7x−7=0

y−x−1=0

y=x+1

Substituting the value of x in first equation, we get;

5x+7y−15=2xy

Or, 5x+7x+7−15−2x(x+1) Or, 12x−8=2x

2

+2x Or, 10x−8=2x

2

Or, x

2

=5x−4

Similarly, substituting the value of y in second equation, we get;

7y−x−11=xy

Or, 7x+7−x−11=x

2

+1 Or, 6x−5=x

2

From above two equations, it is clear

5x−4=6x−5

Or, 5x+1=6x

Or, x=1

Hence, y=x+1=2

Hence, x=1 and y=2