27/x-2+31/y-3=85,31/x-2+27/y+3=89
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27/x-2+31/y-3=85
= 27/x+31/y=85+2+3=90 ---case 1
31/x-2+27/y+3=89
31/x+27/y=89+1=90 -----case2
This shows case 1 and 2 are equal.
27/x+31/y=31/x+27/y
=31/y-27/y=31/x-27/x. [by transposing]
=4/y=4/x
=4x=4y. [by cross multiplying]
=x=y. [dividing both sides by 4]
= 27/x+31/y=85+2+3=90 ---case 1
31/x-2+27/y+3=89
31/x+27/y=89+1=90 -----case2
This shows case 1 and 2 are equal.
27/x+31/y=31/x+27/y
=31/y-27/y=31/x-27/x. [by transposing]
=4/y=4/x
=4x=4y. [by cross multiplying]
=x=y. [dividing both sides by 4]
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