Solve 4y(1000-x)=1000y(x)

$$4y(1000-x)=1000y(x)$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{1000}{251}\approx 3.984063745\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by 1000-x.

$$4000y-4xy=1000yx$$

Subtract 1000yx from both sides.

$$4000y-4xy-1000yx=0$$

Combine -4xy and -1000yx to get -1004xy.

$$4000y-1004xy=0$$

Subtract 4000y from both sides. Anything subtracted from zero gives its negation.

$$-1004xy=-4000y$$

The equation is in standard form.

$$\left(-1004y\right)x=-4000y$$

Divide both sides by -1004y.

$$\frac{\left(-1004y\right)x}{-1004y}=-\frac{4000y}{-1004y}$$

Dividing by -1004y undoes the multiplication by -1004y.

$$x=-\frac{4000y}{-1004y}$$

Divide -4000y by -1004y.

$$x=\frac{1000}{251}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=\frac{1000}{251}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by 1000-x.

$$4000y-4xy=1000yx$$

Subtract 1000yx from both sides.

$$4000y-4xy-1000yx=0$$

Combine -4xy and -1000yx to get -1004xy.

$$4000y-1004xy=0$$

Combine all terms containing y.

$$\left(4000-1004x\right)y=0$$

Divide 0 by 4000-1004x.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{1000}{251}\approx 3.984063745\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by 1000-x.

$$4000y-4xy=1000yx$$

Subtract 1000yx from both sides.

$$4000y-4xy-1000yx=0$$

Combine -4xy and -1000yx to get -1004xy.

$$4000y-1004xy=0$$

Subtract 4000y from both sides. Anything subtracted from zero gives its negation.

$$-1004xy=-4000y$$

The equation is in standard form.

$$\left(-1004y\right)x=-4000y$$

Divide both sides by -1004y.

$$\frac{\left(-1004y\right)x}{-1004y}=-\frac{4000y}{-1004y}$$

Dividing by -1004y undoes the multiplication by -1004y.

$$x=-\frac{4000y}{-1004y}$$

Divide -4000y by -1004y.

$$x=\frac{1000}{251}$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=\frac{1000}{251}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by 1000-x.

$$4000y-4xy=1000yx$$

Subtract 1000yx from both sides.

$$4000y-4xy-1000yx=0$$

Combine -4xy and -1000yx to get -1004xy.

$$4000y-1004xy=0$$

Combine all terms containing y.

$$\left(4000-1004x\right)y=0$$

Divide 0 by 4000-1004x.

$$y=0$$