Solve x(y-2)-y(x-3)=-14

$$x(y-2)-y(x-3)=-14$$

Solve for x

$$x=\frac{3y}{2}+7$$

Steps for Solving Linear Equation

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

$$xy-2x-y\left(x-3\right)=-14$$

Use the distributive property to multiply y by x-3.

$$xy-2x-\left(yx-3y\right)=-14$$

To find the opposite of yx-3y, find the opposite of each term.

$$xy-2x-yx+3y=-14$$

Combine xy and -yx to get 0.

$$-2x+3y=-14$$

Subtract 3y from both sides.

$$-2x=-14-3y$$

The equation is in standard form.

$$-2x=-3y-14$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{-3y-14}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{-3y-14}{-2}$$

Divide -14-3y by -2.

$$x=\frac{3y}{2}+7$$

Solve for y

$$y=\frac{2\left(x-7\right)}{3}$$

Steps for Solving Linear Equation

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

$$xy-2x-y\left(x-3\right)=-14$$

Use the distributive property to multiply y by x-3.

$$xy-2x-\left(yx-3y\right)=-14$$

To find the opposite of yx-3y, find the opposite of each term.

$$xy-2x-yx+3y=-14$$

Combine xy and -yx to get 0.

$$-2x+3y=-14$$

Add 2x to both sides.

$$3y=-14+2x$$

The equation is in standard form.

$$3y=2x-14$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{2x-14}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{2x-14}{3}$$