Solve kx+2y=pqquad1

$$k x + 2 y = p q \quad 1$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{pq_{1}-2y}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=\frac{pq_{1}}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2y from both sides.

$$kx=pq_{1}-2y$$

The equation is in standard form.

$$xk=pq_{1}-2y$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{pq_{1}-2y}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{pq_{1}-2y}{x}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{kx+2y}{q_{1}}\text{, }&q_{1}\neq 0\\p\in \mathrm{C}\text{, }&y=-\frac{kx}{2}\text{ and }q_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$pq_{1}=kx+2y$$

The equation is in standard form.

$$q_{1}p=kx+2y$$

Divide both sides by q_{1}.

$$\frac{q_{1}p}{q_{1}}=\frac{kx+2y}{q_{1}}$$

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

$$p=\frac{kx+2y}{q_{1}}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{pq_{1}-2y}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=\frac{pq_{1}}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2y from both sides.

$$kx=pq_{1}-2y$$

The equation is in standard form.

$$xk=pq_{1}-2y$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{pq_{1}-2y}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{pq_{1}-2y}{x}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{kx+2y}{q_{1}}\text{, }&q_{1}\neq 0\\p\in \mathrm{R}\text{, }&y=-\frac{kx}{2}\text{ and }q_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$pq_{1}=kx+2y$$

The equation is in standard form.

$$q_{1}p=kx+2y$$

Divide both sides by q_{1}.

$$\frac{q_{1}p}{q_{1}}=\frac{kx+2y}{q_{1}}$$

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

$$p=\frac{kx+2y}{q_{1}}$$