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Question

Solve the following systems of equations by the method of cross-multiplication:
5x+y2xy=1
15x+y+7xy=10
where x0 , y0 and xy

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Solution

Substitute 1x+y=a and 1xy=b
We get equations as follows: 5a2b+1=0 and 15a+7b10=0

Using method of cross-multiplication we get:

a(2)(10)(7)(1)=b(1)(15)(10)(5)=1(5)(7)(15)(2)

a13=b65=165

From a13=165 we get a=15

Similarly b=1

Resubstituting values of a and b we get x+y=5 and xy=1

Adding these 2 equations gives us x=3 .

Substracting 2nd equation from 1st gives us y=2

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