148/x + 231/y = 527/xy , 231/x + 148/y = 610/xy

Solve simultaneous equations

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Solution

Given (148/x) + (231/y) = (527/xy)
⇒(148y + 231x) / xy = (527/ xy)
∴231x+148y = 527 → (1)

231/x + 148/y = 610/xy
⇒ (231y + 148x)/xy = 610/xy
∴148x+231y=610 → (2)
Multiply (1) with 148 and (2) with 231
31488x+21904y=77996 → (3)
34188x+53361y=140910 →(4)
Subtract (3) from (4), we get
34188x+53361y=140910
31488x+21904y=77996
31457y=62914
∴y=2
Put y=2 in (1)
231x+148(2)=527
⇒231x=527-296=231
∴x=1

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