The real numbers x and y satisfy the nonlinear system of equations

Question

2x^2−6xy+2y^2+43x+43y=174 &
x^2+y^2+5x+5y=30.
Find the largest possible value of |xy|.

Answer 1

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Answer 2

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.