Question

Solve the following pairs of equations reducing them to a pairs of linear equation 99x+101y=499xy 101x+99y=501xy

Answer 1

let 1/x=m, 1/y=n
99x+101y=499xy---------1
101x+99y=501xy----------2
dividing both equations by xy
99/y+101/x=499
or 101m+99n=499--------3

101/y +99/x=501
or 99m+101n= 501---------4
3 + 4
200m+200n=1000
or 200(m+n)=1000
or m+n = 1000/200
or m+n =5 ---------------5
3 - 4
2m-2n= -2
or 2(m-n). = -2
or m-n= -2/2
or m- n= -1-----------------6
5+6
2m=4
or m = 2
or 1/x =2
or x= 1/2 (Answer)
5-6
2n=6
or n= 3
or 1/y=3
or y= 1/3 (answer)
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