y=50+40x+30y-5x^2-4y^2-3xy

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Solution for y=50+40x+30y-5x^2-4y^2-3xy equation: 


Simplifying
y = 50 + 40x + 30y + -5x2 + -4y2 + -3xy

Reorder the terms:
y = 50 + 40x + -3xy + -5x2 + 30y + -4y2

Solving
y = 50 + 40x + -3xy + -5x2 + 30y + -4y2

Solving for variable 'y'.

Reorder the terms:
-50 + -40x + 3xy + 5x2 + y + -30y + 4y2 = 50 + 40x + -3xy + -5x2 + 30y + -4y2 + -50 + -40x + 3xy + 5x2 + -30y + 4y2

Combine like terms: y + -30y = -29y
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 50 + 40x + -3xy + -5x2 + 30y + -4y2 + -50 + -40x + 3xy + 5x2 + -30y + 4y2

Reorder the terms:
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 50 + -50 + 40x + -40x + -3xy + 3xy + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2

Combine like terms: 50 + -50 = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0 + 40x + -40x + -3xy + 3xy + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 40x + -40x + -3xy + 3xy + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2

Combine like terms: 40x + -40x = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0 + -3xy + 3xy + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = -3xy + 3xy + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2

Combine like terms: -3xy + 3xy = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0 + -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = -5x2 + 5x2 + 30y + -30y + -4y2 + 4y2

Combine like terms: -5x2 + 5x2 = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0 + 30y + -30y + -4y2 + 4y2
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 30y + -30y + -4y2 + 4y2

Combine like terms: 30y + -30y = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0 + -4y2 + 4y2
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
-50 + -40x + 3xy + 5x2 + -29y + 4y2 = 0

The solution to this equation could not be determined.

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