Solve =ax+bx=c

$$= a x + b x = c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax=c-bx$$

The equation is in standard form.

$$xa=c-bx$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide c-bx by x.

$$a=-b+\frac{c}{x}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx=c-ax$$

The equation is in standard form.

$$xb=c-ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{c-ax}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide c-ax by x.

$$b=-a+\frac{c}{x}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax=c-bx$$

The equation is in standard form.

$$xa=c-bx$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide c-bx by x.

$$a=-b+\frac{c}{x}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$bx=c-ax$$

The equation is in standard form.

$$xb=c-ax$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{c-ax}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide c-ax by x.

$$b=-a+\frac{c}{x}$$