Solve 200-x(4y)=x(200-y)

$$200 - x ( 4 y ) = x ( 200 - y )$$

Solve for x

$$x=\frac{200}{3y+200}$$

$$y\neq -\frac{200}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 200-y.

$$200-x\times 4y=200x-xy$$

Subtract 200x from both sides.

$$200-x\times 4y-200x=-xy$$

Add xy to both sides.

$$200-x\times 4y-200x+xy=0$$

Multiply -1 and 4 to get -4.

$$200-4xy-200x+xy=0$$

Combine -4xy and xy to get -3xy.

$$200-3xy-200x=0$$

Subtract 200 from both sides. Anything subtracted from zero gives its negation.

$$-3xy-200x=-200$$

Combine all terms containing x.

$$\left(-3y-200\right)x=-200$$

Divide both sides by -3y-200.

$$\frac{\left(-3y-200\right)x}{-3y-200}=-\frac{200}{-3y-200}$$

Dividing by -3y-200 undoes the multiplication by -3y-200.

$$x=-\frac{200}{-3y-200}$$

Divide -200 by -3y-200.

$$x=\frac{200}{3y+200}$$

Solve for y

$$y=-\frac{200}{3}+\frac{200}{3x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 200-y.

$$200-x\times 4y=200x-xy$$

Add xy to both sides.

$$200-x\times 4y+xy=200x$$

Multiply -1 and 4 to get -4.

$$200-4xy+xy=200x$$

Combine -4xy and xy to get -3xy.

$$200-3xy=200x$$

Subtract 200 from both sides.

$$-3xy=200x-200$$

The equation is in standard form.

$$\left(-3x\right)y=200x-200$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)y}{-3x}=\frac{200x-200}{-3x}$$

Dividing by -3x undoes the multiplication by -3x.

$$y=\frac{200x-200}{-3x}$$

Divide -200+200x by -3x.

$$y=-\frac{200}{3}+\frac{200}{3x}$$