Question

решить систему уравнений {3х^2y^2 +x^2 - 3хy = 7 и 10х^2y^2 +3x^2 - 20хy = 3

Answer 1

Відповідь:

The given system of equations can be solved using substitution.

First, isolate the x terms in the first equation by subtracting 3xy from both sides:

3x^2y^2 + x^2 - 3xy = 7 - 3xy x^2(3y^2 + 1) - 3xy = 7 - 3xy x^2 = (7 - 3xy) / (3y^2 + 1)

Next, substitute this expression for x^2 in the second equation:

10x^2y^2 + 3x^2 - 20xy = 3 10x^2y^2 + (7 - 3xy) / (3y^2 + 1) - 20xy = 3

Finally, solve for y:

10y^2(7 - 3xy) + 3(7 - 3xy) - 20xy = 3(3y^2 + 1) 70y^2 - 30xy^2 - 21 + 9xy = 9y^2 + 3 61y^2 - 30xy^2 + 9xy = 3 y^2(61 - 30x) + xy(9 - 30) = 3 y = (3 - xy(9 - 30)) / (61 - 30x)

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