Question

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

Answer 1

Solution

Let
x−1
1
​
=X and
y−2
1
​
=Y
Hence, the given equations are reduced to:
5X+Y=2 ....(1)
6X−3Y=1 ....(2)
Multiplying (1) by 3, we get
15X+3Y=6 ....(3)
Adding (3) and (2), we get
21X=7
⇒X=
3
1
​

Substitute this value of X in (2), we get
6(
3
1
​
)−3Y=1
⇒2−3Y=1
⇒3Y=1
⇒Y=
3
1
​


Resubstitute the values of X and Y to get x and y,
X=
x−1
1
​

⇒
3
1
​
=
x−1
1
​

⇒x−1=3
⇒x=4
Y=
y−2
1
​

⇒
3
1
​
=
y−2
1
​

⇒y−2=3
⇒y=5