Solve (160-2x)=2x(80-2y)

$$( 160 - 2 x ) = 2 x ( 80 - 2 y )$$

Solve for x

$$x=-\frac{80}{2y-81}$$

$$y\neq \frac{81}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by 80-2y.

$$160-2x=160x-4xy$$

Subtract 160x from both sides.

$$160-2x-160x=-4xy$$

Combine -2x and -160x to get -162x.

$$160-162x=-4xy$$

Add 4xy to both sides.

$$160-162x+4xy=0$$

Subtract 160 from both sides. Anything subtracted from zero gives its negation.

$$-162x+4xy=-160$$

Combine all terms containing x.

$$\left(-162+4y\right)x=-160$$

The equation is in standard form.

$$\left(4y-162\right)x=-160$$

Divide both sides by 4y-162.

$$\frac{\left(4y-162\right)x}{4y-162}=-\frac{160}{4y-162}$$

Dividing by 4y-162 undoes the multiplication by 4y-162.

$$x=-\frac{160}{4y-162}$$

Divide -160 by 4y-162.

$$x=-\frac{80}{2y-81}$$

Solve for y

$$y=\frac{81}{2}-\frac{40}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by 80-2y.

$$160-2x=160x-4xy$$

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

$$160x-4xy=160-2x$$

Subtract 160x from both sides.

$$-4xy=160-2x-160x$$

Combine -2x and -160x to get -162x.

$$-4xy=160-162x$$

The equation is in standard form.

$$\left(-4x\right)y=160-162x$$

Divide both sides by -4x.

$$\frac{\left(-4x\right)y}{-4x}=\frac{160-162x}{-4x}$$

Dividing by -4x undoes the multiplication by -4x.

$$y=\frac{160-162x}{-4x}$$

Divide 160-162x by -4x.

$$y=\frac{81}{2}-\frac{40}{x}$$