Solve (x+5)(y+1)=(x+8)(y-3)

$$(x+5)(y+1)=(x+8)(y-3)$$

Solve for x

$$x=\frac{3y-29}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by y+1.

$$xy+x+5y+5=\left(x+8\right)\left(y-3\right)$$

Use the distributive property to multiply x+8 by y-3.

$$xy+x+5y+5=xy-3x+8y-24$$

Subtract xy from both sides.

$$xy+x+5y+5-xy=-3x+8y-24$$

Combine xy and -xy to get 0.

$$x+5y+5=-3x+8y-24$$

Add 3x to both sides.

$$x+5y+5+3x=8y-24$$

Combine x and 3x to get 4x.

$$4x+5y+5=8y-24$$

Subtract 5y from both sides.

$$4x+5=8y-24-5y$$

Combine 8y and -5y to get 3y.

$$4x+5=3y-24$$

Subtract 5 from both sides.

$$4x=3y-24-5$$

Subtract 5 from -24 to get -29.

$$4x=3y-29$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{3y-29}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{3y-29}{4}$$

Solve for y

$$y=\frac{4x+29}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by y+1.

$$xy+x+5y+5=\left(x+8\right)\left(y-3\right)$$

Use the distributive property to multiply x+8 by y-3.

$$xy+x+5y+5=xy-3x+8y-24$$

Subtract xy from both sides.

$$xy+x+5y+5-xy=-3x+8y-24$$

Combine xy and -xy to get 0.

$$x+5y+5=-3x+8y-24$$

Subtract 8y from both sides.

$$x+5y+5-8y=-3x-24$$

Combine 5y and -8y to get -3y.

$$x-3y+5=-3x-24$$

Subtract x from both sides.

$$-3y+5=-3x-24-x$$

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

$$-3y+5=-4x-24$$

Subtract 5 from both sides.

$$-3y=-4x-24-5$$

Subtract 5 from -24 to get -29.

$$-3y=-4x-29$$

Divide both sides by -3.

$$\frac{-3y}{-3}=\frac{-4x-29}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$y=\frac{-4x-29}{-3}$$

Divide -4x-29 by -3.

$$y=\frac{4x+29}{3}$$