Solve z=x+y/x+4

$$z = \frac { x + y } { x + 4 }$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{4z-y}{z-1}\text{, }&y\neq 4\text{ and }z\neq 1\\x\neq -4\text{, }&z=1\text{ and }y=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.

$$z\left(x+4\right)=x+y$$

Use the distributive property to multiply z by x+4.

$$zx+4z=x+y$$

Subtract x from both sides.

$$zx+4z-x=y$$

Subtract 4z from both sides.

$$zx-x=y-4z$$

Combine all terms containing x.

$$\left(z-1\right)x=y-4z$$

Divide both sides by z-1.

$$\frac{\left(z-1\right)x}{z-1}=\frac{y-4z}{z-1}$$

Dividing by z-1 undoes the multiplication by z-1.

$$x=\frac{y-4z}{z-1}$$

Variable x cannot be equal to -4.

$$x=\frac{y-4z}{z-1}\text{, }x\neq -4$$

Solve for y

$$y=xz-x+4z$$

$$x\neq -4$$

Solution Steps

Multiply both sides of the equation by x+4.

$$z\left(x+4\right)=x+y$$

Use the distributive property to multiply z by x+4.

$$zx+4z=x+y$$

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

$$x+y=zx+4z$$

Subtract x from both sides.

$$y=zx+4z-x$$