Solve 2(xy+8x+8y)=2(9x)+2(9y)

$$2(xy+8x+8y)=2(9x)+2(9y)$$

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by xy+8x+8y.

$$2xy+16x+16y=2\times 9x+2\times 9y$$

Do the multiplications.

$$2xy+16x+16y=18x+18y$$

Subtract 18x from both sides.

$$2xy+16x+16y-18x=18y$$

Combine 16x and -18x to get -2x.

$$2xy-2x+16y=18y$$

Subtract 16y from both sides.

$$2xy-2x=18y-16y$$

Combine 18y and -16y to get 2y.

$$2xy-2x=2y$$

Combine all terms containing x.

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

Divide both sides by 2y-2.

$$\frac{\left(2y-2\right)x}{2y-2}=\frac{2y}{2y-2}$$

Dividing by 2y-2 undoes the multiplication by 2y-2.

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

Divide 2y by 2y-2.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by xy+8x+8y.

$$2xy+16x+16y=2\times 9x+2\times 9y$$

Do the multiplications.

$$2xy+16x+16y=18x+18y$$

Subtract 18y from both sides.

$$2xy+16x+16y-18y=18x$$

Combine 16y and -18y to get -2y.

$$2xy+16x-2y=18x$$

Subtract 16x from both sides.

$$2xy-2y=18x-16x$$

Combine 18x and -16x to get 2x.

$$2xy-2y=2x$$

Combine all terms containing y.

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

Divide both sides by 2x-2.

$$\frac{\left(2x-2\right)y}{2x-2}=\frac{2x}{2x-2}$$

Dividing by 2x-2 undoes the multiplication by 2x-2.

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

Divide 2x by 2x-2.

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