Solve y=2y-x/1+y

$$y = \frac { 2 y - x } { 1 + y }$$

Solve for x

$$x=y\left(1-y\right)$$

$$y\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+1.

$$y\left(y+1\right)=2y-x$$

Use the distributive property to multiply y by y+1.

$$y^{2}+y=2y-x$$

Swap sides so that all variable terms are on the left hand side.

$$2y-x=y^{2}+y$$

Subtract 2y from both sides.

$$-x=y^{2}+y-2y$$

Combine y and -2y to get -y.

$$-x=y^{2}-y$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{y\left(y-1\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{y\left(y-1\right)}{-1}$$

Divide y\left(-1+y\right) by -1.

$$x=-y\left(y-1\right)$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{\sqrt{1-4x}+1}{2}\text{, }&\text{unconditionally}\\y=\frac{-\sqrt{1-4x}+1}{2}\text{, }&x\neq -2\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{-\sqrt{1-4x}+1}{2}\text{, }&x\neq -2\text{ and }x\leq \frac{1}{4}\\y=\frac{\sqrt{1-4x}+1}{2}\text{, }&x\leq \frac{1}{4}\end{matrix}\right.$$