Solve 3.2x=(x+3x)y

$$3.2x=(x+3x)y$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=\frac{4}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine x and 3x to get 4x.

$$3.2x=4xy$$

Subtract 4xy from both sides.

$$3.2x-4xy=0$$

Combine all terms containing x.

$$\left(3.2-4y\right)x=0$$

Divide 0 by 3.2-4y.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0.8\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine x and 3x to get 4x.

$$3.2x=4xy$$

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

$$4xy=3.2x$$

The equation is in standard form.

$$4xy=\frac{16x}{5}$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{16x}{5\times 4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{16x}{5\times 4x}$$

Divide \frac{16x}{5} by 4x.

$$y=\frac{4}{5}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=\frac{4}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine x and 3x to get 4x.

$$3.2x=4xy$$

Subtract 4xy from both sides.

$$3.2x-4xy=0$$

Combine all terms containing x.

$$\left(3.2-4y\right)x=0$$

Divide 0 by 3.2-4y.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0.8\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine x and 3x to get 4x.

$$3.2x=4xy$$

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

$$4xy=3.2x$$

The equation is in standard form.

$$4xy=\frac{16x}{5}$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{16x}{5\times 4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{16x}{5\times 4x}$$

Divide \frac{16x}{5} by 4x.

$$y=\frac{4}{5}$$