Solve xy+4x-2y=8

$$x y + 4 x - 2 y = 8$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2y to both sides.

$$xy+4x=8+2y$$

Combine all terms containing x.

$$\left(y+4\right)x=8+2y$$

The equation is in standard form.

$$\left(y+4\right)x=2y+8$$

Divide both sides by 4+y.

$$\frac{\left(y+4\right)x}{y+4}=\frac{2y+8}{y+4}$$

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

$$x=\frac{2y+8}{y+4}$$

Divide 8+2y by 4+y.

$$x=2$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-4\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$xy-2y=8-4x$$

Combine all terms containing y.

$$\left(x-2\right)y=8-4x$$

Divide both sides by -2+x.

$$\frac{\left(x-2\right)y}{x-2}=\frac{8-4x}{x-2}$$

Dividing by -2+x undoes the multiplication by -2+x.

$$y=\frac{8-4x}{x-2}$$

Divide 8-4x by -2+x.

$$y=-4$$

Solve for x

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2y to both sides.

$$xy+4x=8+2y$$

Combine all terms containing x.

$$\left(y+4\right)x=8+2y$$

The equation is in standard form.

$$\left(y+4\right)x=2y+8$$

Divide both sides by 4+y.

$$\frac{\left(y+4\right)x}{y+4}=\frac{2y+8}{y+4}$$

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

$$x=\frac{2y+8}{y+4}$$

Divide 8+2y by 4+y.

$$x=2$$

Solve for y

$$\left\{\begin{matrix}\\y=-4\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$xy-2y=8-4x$$

Combine all terms containing y.

$$\left(x-2\right)y=8-4x$$

Divide both sides by -2+x.

$$\frac{\left(x-2\right)y}{x-2}=\frac{8-4x}{x-2}$$

Dividing by -2+x undoes the multiplication by -2+x.

$$y=\frac{8-4x}{x-2}$$

Divide 8-4x by -2+x.

$$y=-4$$