Solve y_{3}x=4y+1

$$y _ { 3 } x = 4 y + 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{4y+1}{y_{3}}\text{, }&y_{3}\neq 0\\x\in \mathrm{C}\text{, }&y=-\frac{1}{4}\text{ and }y_{3}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$y_{3}x=4y+1$$

Divide both sides by y_{3}.

$$\frac{y_{3}x}{y_{3}}=\frac{4y+1}{y_{3}}$$

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

$$x=\frac{4y+1}{y_{3}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{4y+1}{y_{3}}\text{, }&y_{3}\neq 0\\x\in \mathrm{R}\text{, }&y=-\frac{1}{4}\text{ and }y_{3}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$y_{3}x=4y+1$$

Divide both sides by y_{3}.

$$\frac{y_{3}x}{y_{3}}=\frac{4y+1}{y_{3}}$$

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

$$x=\frac{4y+1}{y_{3}}$$

Solve for y

$$y=\frac{xy_{3}-1}{4}$$

Steps for Solving Linear Equation

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

$$4y+1=y_{3}x$$

Subtract 1 from both sides.

$$4y=y_{3}x-1$$

The equation is in standard form.

$$4y=xy_{3}-1$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{xy_{3}-1}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{xy_{3}-1}{4}$$