Solve left(x-5right)left(y+3right)=xy-9

$$\left( x-5 \right) \left( y+3 \right) =xy-9$$

Solve for x

$$x=\frac{5y}{3}+2$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-5 by y+3.

$$xy+3x-5y-15=xy-9$$

Subtract xy from both sides.

$$xy+3x-5y-15-xy=-9$$

Combine xy and -xy to get 0.

$$3x-5y-15=-9$$

Add 5y to both sides.

$$3x-15=-9+5y$$

Add 15 to both sides.

$$3x=-9+5y+15$$

Add -9 and 15 to get 6.

$$3x=6+5y$$

The equation is in standard form.

$$3x=5y+6$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{5y+6}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{5y+6}{3}$$

Divide 6+5y by 3.

$$x=\frac{5y}{3}+2$$

Solve for y

$$y=\frac{3\left(x-2\right)}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-5 by y+3.

$$xy+3x-5y-15=xy-9$$

Subtract xy from both sides.

$$xy+3x-5y-15-xy=-9$$

Combine xy and -xy to get 0.

$$3x-5y-15=-9$$

Subtract 3x from both sides.

$$-5y-15=-9-3x$$

Add 15 to both sides.

$$-5y=-9-3x+15$$

Add -9 and 15 to get 6.

$$-5y=6-3x$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{6-3x}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{6-3x}{-5}$$

Divide 6-3x by -5.

$$y=\frac{3x-6}{5}$$