Solve ax+bg=c

$$a x + b g = c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract bg from both sides.

$$ax=c-bg$$

The equation is in standard form.

$$xa=c-bg$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{c-bg}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{c-bg}{x}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bg=c-ax$$

The equation is in standard form.

$$gb=c-ax$$

Divide both sides by g.

$$\frac{gb}{g}=\frac{c-ax}{g}$$

Dividing by g undoes the multiplication by g.

$$b=\frac{c-ax}{g}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract bg from both sides.

$$ax=c-bg$$

The equation is in standard form.

$$xa=c-bg$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{c-bg}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{c-bg}{x}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bg=c-ax$$

The equation is in standard form.

$$gb=c-ax$$

Divide both sides by g.

$$\frac{gb}{g}=\frac{c-ax}{g}$$

Dividing by g undoes the multiplication by g.

$$b=\frac{c-ax}{g}$$