Solve x/y+z=4x

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{yz}{1-4y}\text{, }&y\neq \frac{1}{4}\text{ and }y\neq 0\\x\in \mathrm{C}\text{, }&y=\frac{1}{4}\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$x+yz=4xy$$

Subtract 4xy from both sides.

$$x+yz-4xy=0$$

Subtract yz from both sides. Anything subtracted from zero gives its negation.

$$x-4xy=-yz$$

Reorder the terms.

$$-4xy+x=-yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -4y+1.

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

Dividing by -4y+1 undoes the multiplication by -4y+1.

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{yz}{1-4y}\text{, }&y\neq \frac{1}{4}\text{ and }y\neq 0\\x\in \mathrm{R}\text{, }&y=\frac{1}{4}\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$x+yz=4xy$$

Subtract 4xy from both sides.

$$x+yz-4xy=0$$

Subtract yz from both sides. Anything subtracted from zero gives its negation.

$$x-4xy=-yz$$

Reorder the terms.

$$-4xy+x=-yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -4y+1.

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

Dividing by -4y+1 undoes the multiplication by -4y+1.

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

Solve for y

$$\left\{\begin{matrix}y=-\frac{x}{z-4x}\text{, }&x\neq 0\text{ and }x\neq \frac{z}{4}\\y\neq 0\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$x+yz=4xy$$

Subtract 4xy from both sides.

$$x+yz-4xy=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$yz-4xy=-x$$

Combine all terms containing y.

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

Divide both sides by z-4x.

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

Dividing by z-4x undoes the multiplication by z-4x.

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

Variable y cannot be equal to 0.

$$y=-\frac{x}{z-4x}\text{, }y\neq 0$$