Posted by anonymous on Friday, June 21, 2013 at 1:49am.
The real numbers x and y satisfy the nonlinear system of equations
2x^2−6xy+2y^2+43x+43y=174
x^2+y^2+5x+5y=30.
Find the largest possible value of xy.

math  MathMate, Sunday, June 23, 2013 at 1:21pm
This has been posted many times, and answered more than once by different teachers.
The solution to the system of algebraic equations are:
(3,1),(1,3),(2,4),(4,2).
The maximum value of xy is therefore 8.
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