Solve x=1 y=2 x y

Evaluate

{x = 1 \times y 1 \times y = 2 x y

Any expression multiplied by 1 remains the same

{x = y 1 \times y = 2 x y

Any expression multiplied by 1 remains the same

{x = y y = 2 x y

Substitute the given value of x into the equation y = 2 x y

y = 2 y \times y

Simplify

y = 2 y^{2}

Add or subtract both sides

y - 2 y^{2} = 0

Factor the expression

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y (1 - 2 y) = 0

When the product of factors equals 0,at least one factor is 0

y = 0 1 - 2 y = 0

Solve the equation for y

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y = 0 y = \frac{1}{2}

Calculate

y = 0 \cup y = \frac{1}{2}

Rearrange the terms

{x = y y = 0 \cup {x = y y = \frac{1}{2}

Calculate

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{x = 0 y = 0 \cup {x = y y = \frac{1}{2}

Calculate

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{x = 0 y = 0 \cup {x = \frac{1}{2} y = \frac{1}{2}

Check the solution

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{x = 0 y = 0 \cup {x = \frac{1}{2} y = \frac{1}{2}

Check the solution

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{x = 0 y = 0 \cup {x = \frac{1}{2} y = \frac{1}{2}

Solution

(x_{1}, y_{1}) = (0, 0) (x_{2}, y_{2}) = (\frac{1}{2}, \frac{1}{2})

Solve the system of equations