Solve xy_{3}=4x+a

$$x y _ { 3 } = 4 x + a$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$xy_{3}-4x=a$$

Combine all terms containing x.

$$\left(y_{3}-4\right)x=a$$

Divide both sides by y_{3}-4.

$$\frac{\left(y_{3}-4\right)x}{y_{3}-4}=\frac{a}{y_{3}-4}$$

Dividing by y_{3}-4 undoes the multiplication by y_{3}-4.

$$x=\frac{a}{y_{3}-4}$$

Solve for a

$$a=x\left(y_{3}-4\right)$$

Solution Steps

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

$$4x+a=xy_{3}$$

Subtract 4x from both sides.

$$a=xy_{3}-4x$$

Solve for x

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

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$xy_{3}-4x=a$$

Combine all terms containing x.

$$\left(y_{3}-4\right)x=a$$

Divide both sides by y_{3}-4.

$$\frac{\left(y_{3}-4\right)x}{y_{3}-4}=\frac{a}{y_{3}-4}$$

Dividing by y_{3}-4 undoes the multiplication by y_{3}-4.

$$x=\frac{a}{y_{3}-4}$$