SOLUTION: Solve for x and y if 2/x - 3/y = 2 and 4/x + 9/y + 1 = 0

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Question 917720: Solve for x and y if 2/x - 3/y = 2 and 4/x + 9/y + 1 = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
system%282%2Fx+-+3%2Fy+=+2+%2C+4%2Fx+%2B+9%2Fy+%2B+1+=+0%29
With the "change of variable" a=1%2Fx and b=1%2Fy ,
the system of equations turns into
system%282a-3b=2%2C4a%2B9b%2B1=0%29<-->system%282a-3b=2%2C4a%2B9b=-1%29 .
Multiplying the first equation times (-2) we get
-4a%2B6b=-4 ,
and adding that to the second equation, we get
15b=-5-->b=-5%2F15-->b=-1%2F3 .
Substituting that value into 2a-3b=2 we get
2a-3%28-1%2F3%29=2-->2a%2B1=2-->2a=2-1-->2a=1-->a=1%2F2 .
going back to the original variables:
1%2Fx=1%2F2-->x=2
1%2Fy=-1%2F3-->y=-3