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Question

Solve the following system of equations:
x+y=ab
axby=a2+b2

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Solution

The given system of equations may be written as
x+y(ab)=0
axby(a2+b2)=0

By cross-multiplication, we have
x(a2+b2)b(ab)=y(a2+b2)a×(ab)=1ba

xa2ab=yab+b2=1ba

xa(a+b)=yb(a+b)=1(a+b)

x=a(a+b)(a+b)=a and y=b(a+b)(a+b)=b

Hence, x=a,y=b is the solution of the given system of equations.

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