Solve yx-z-4x=3

$$yx-z-4x=3$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{z+3}{y-4}\text{, }&y\neq 4\\x\in \mathrm{C}\text{, }&z=-3\text{ and }y=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Add z to both sides.

$$yx-4x=3+z$$

Combine all terms containing x.

$$\left(y-4\right)x=3+z$$

The equation is in standard form.

$$\left(y-4\right)x=z+3$$

Divide both sides by y-4.

$$\frac{\left(y-4\right)x}{y-4}=\frac{z+3}{y-4}$$

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

$$x=\frac{z+3}{y-4}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{4x+z+3}{x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\text{ and }z=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add z to both sides.

$$yx-4x=3+z$$

Add 4x to both sides.

$$yx=3+z+4x$$

The equation is in standard form.

$$xy=4x+z+3$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{4x+z+3}{x}$$

Dividing by x undoes the multiplication by x.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{z+3}{y-4}\text{, }&y\neq 4\\x\in \mathrm{R}\text{, }&z=-3\text{ and }y=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Add z to both sides.

$$yx-4x=3+z$$

Combine all terms containing x.

$$\left(y-4\right)x=3+z$$

The equation is in standard form.

$$\left(y-4\right)x=z+3$$

Divide both sides by y-4.

$$\frac{\left(y-4\right)x}{y-4}=\frac{z+3}{y-4}$$

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

$$x=\frac{z+3}{y-4}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{4x+z+3}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add z to both sides.

$$yx-4x=3+z$$

Add 4x to both sides.

$$yx=3+z+4x$$

The equation is in standard form.

$$xy=4x+z+3$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{4x+z+3}{x}$$

Dividing by x undoes the multiplication by x.

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