Solve omega=ax+by

$$\omega = a x + b y$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$ax+by=\omega$$

Subtract by from both sides.

$$ax=\omega -by$$

The equation is in standard form.

$$xa=\omega -by$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\omega -by}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\omega -by}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ax-\omega }{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\omega =ax\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax+by=\omega$$

Subtract ax from both sides.

$$by=\omega -ax$$

The equation is in standard form.

$$yb=\omega -ax$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{\omega -ax}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{\omega -ax}{y}$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax+by=\omega$$

Subtract by from both sides.

$$ax=\omega -by$$

The equation is in standard form.

$$xa=\omega -by$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\omega -by}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\omega -by}{x}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax-\omega }{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\omega =ax\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax+by=\omega$$

Subtract ax from both sides.

$$by=\omega -ax$$

The equation is in standard form.

$$yb=\omega -ax$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{\omega -ax}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{\omega -ax}{y}$$