Solve the following equation.
$x^{2} - 4 x y + 4 y^{2} = 0, x^{2} - 2 y^{2} - 2 = 0$ .

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Solution

Eliminating the constant term by multiplying $2$ nd equation by $2$ and subtracting from $1$ st
$∴ x^{2} - 4 x y + 4 y^{2} = 0$ or $(x - 2 y)^{2} = 0$
$∴ x = 2 y$
Putting in $2$ nd, we get
$4 y^{2} - 2 y^{2} = 2$
$∴ y^{2} = 1$
$∴ y = 1, - 1$
$∴ x = 2, - 2$ .
You may also follow homogenous method.

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