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Consider 1/x= a and 1/2y =b
so,
in first equation,
1/2x=a/2
so first equation can be written as:
a/2 - b +2=0
(a-2b)/2 + 2=0 (taking lcm)
a-2b = -1
similarly, 2nd equation can be written as:
a-b -1=0
a-b=1
Solving both equations using Elemination method,
subtracting them:
a-2b=-1
a - b= 1
-b=-2
so, b=2
so, a-b=1
a-2=1
a=3
Putting a and b values,
a=1/x
3=1/x
so, x=1/3
and b=1/2y
2=1/2y
2y=1/2
y= 1/4
so, x=1/3 and y=1/4
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