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|.
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.