Solve ax+by+c=d

$$a x + b y + c = d$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract by from both sides.

$$ax+c=d-by$$

Subtract c from both sides.

$$ax=d-by-c$$

The equation is in standard form.

$$xa=-by+d-c$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{-by+d-c}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{-by+d-c}{x}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$by+c=d-ax$$

Subtract c from both sides.

$$by=d-ax-c$$

The equation is in standard form.

$$yb=-ax+d-c$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{-ax+d-c}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{-ax+d-c}{y}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract by from both sides.

$$ax+c=d-by$$

Subtract c from both sides.

$$ax=d-by-c$$

The equation is in standard form.

$$xa=-by+d-c$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{-by+d-c}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{-by+d-c}{x}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$by+c=d-ax$$

Subtract c from both sides.

$$by=d-ax-c$$

The equation is in standard form.

$$yb=-ax+d-c$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{-ax+d-c}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{-ax+d-c}{y}$$