Solve y=2000x-x^2quady

$$y = 2000 x - x ^ { 2 } \quad y$$

Solve for y (complex solution)

$$y=\frac{2000x}{x^{2}+1}$$

$$x\neq -i\text{ and }x\neq i$$

Steps for Solving Linear Equation

Add x^{2}y to both sides.

$$y+x^{2}y=2000x$$

Combine all terms containing y.

$$\left(1+x^{2}\right)y=2000x$$

The equation is in standard form.

$$\left(x^{2}+1\right)y=2000x$$

Divide both sides by 1+x^{2}.

$$\frac{\left(x^{2}+1\right)y}{x^{2}+1}=\frac{2000x}{x^{2}+1}$$

Dividing by 1+x^{2} undoes the multiplication by 1+x^{2}.

$$y=\frac{2000x}{x^{2}+1}$$

Solve for y

$$y=\frac{2000x}{x^{2}+1}$$

Steps for Solving Linear Equation

Add x^{2}y to both sides.

$$y+x^{2}y=2000x$$

Combine all terms containing y.

$$\left(1+x^{2}\right)y=2000x$$

The equation is in standard form.

$$\left(x^{2}+1\right)y=2000x$$

Divide both sides by 1+x^{2}.

$$\frac{\left(x^{2}+1\right)y}{x^{2}+1}=\frac{2000x}{x^{2}+1}$$

Dividing by 1+x^{2} undoes the multiplication by 1+x^{2}.

$$y=\frac{2000x}{x^{2}+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1000000-y^{2}}+1000}{y}\text{; }x=\frac{-\sqrt{1000000-y^{2}}+1000}{y}\text{, }&y\neq 0\\x=0\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1000000-y^{2}}+1000}{y}\text{; }x=\frac{-\sqrt{1000000-y^{2}}+1000}{y}\text{, }&y\neq 0\text{ and }|y|\leq 1000\\x=0\text{, }&y=0\end{matrix}\right.$$