How to find x and y in simultaneous equations? y^2-4xy+4y=1 3x^2-2xy=1

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We have to solve the simultaneous equation

y^2 - 4xy + 4y = 1 ...(1)

3x^2 - 2xy = 1 ...(2)

We see that it is not possible to isolate x in terms of y or y in terms of x using any of the equations.

In (1) we get y = 1/(y - 4x + 4)

In (2) we get x = 1/(3x - 2y)

As this is the case, we cannot the solve the system of simultaneous equations. Using a random solution of (1 , 1), we do get both

y^2 - 4xy + 4y = 1 and 3x^2 - 2xy = 1

The required solution of the equations is (1, 1)

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