Solve dx/ay_{1}=k

$$\frac { d x } { a y _ { 1 } } = k$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{aky_{1}}{x}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }y_{1}\neq 0\\d\in \mathrm{C}\text{, }&k=0\text{ and }x=0\text{ and }a\neq 0\text{ and }y_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ay_{1}.

$$dx=kay_{1}$$

Reorder the terms.

$$dx=aky_{1}$$

The equation is in standard form.

$$xd=aky_{1}$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{aky_{1}}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{aky_{1}}{x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{dx}{ky_{1}}\text{, }&x\neq 0\text{ and }d\neq 0\text{ and }y_{1}\neq 0\text{ and }k\neq 0\\a\neq 0\text{, }&\left(x=0\text{ or }d=0\right)\text{ and }k=0\text{ and }y_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ay_{1}.

$$dx=kay_{1}$$

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

$$kay_{1}=dx$$

The equation is in standard form.

$$ky_{1}a=dx$$

Divide both sides by ky_{1}.

$$\frac{ky_{1}a}{ky_{1}}=\frac{dx}{ky_{1}}$$

Dividing by ky_{1} undoes the multiplication by ky_{1}.

$$a=\frac{dx}{ky_{1}}$$

Variable a cannot be equal to 0.

$$a=\frac{dx}{ky_{1}}\text{, }a\neq 0$$

Solve for d

$$\left\{\begin{matrix}d=\frac{aky_{1}}{x}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }y_{1}\neq 0\\d\in \mathrm{R}\text{, }&k=0\text{ and }x=0\text{ and }a\neq 0\text{ and }y_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ay_{1}.

$$dx=kay_{1}$$

Reorder the terms.

$$dx=aky_{1}$$

The equation is in standard form.

$$xd=aky_{1}$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{aky_{1}}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{aky_{1}}{x}$$