Solve bx+ay=ab

$$b x + a y = a b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx}{y-b}\text{, }&b\neq y\\a\in \mathrm{C}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=y\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bx+ay-ab=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ay-ab=-bx$$

Combine all terms containing a.

$$\left(y-b\right)a=-bx$$

Divide both sides by y-b.

$$\frac{\left(y-b\right)a}{y-b}=-\frac{bx}{y-b}$$

Dividing by y-b undoes the multiplication by y-b.

$$a=-\frac{bx}{y-b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ay}{x-a}\text{, }&x\neq a\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=a\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bx+ay-ab=0$$

Subtract ay from both sides. Anything subtracted from zero gives its negation.

$$bx-ab=-ay$$

Combine all terms containing b.

$$\left(x-a\right)b=-ay$$

Divide both sides by x-a.

$$\frac{\left(x-a\right)b}{x-a}=-\frac{ay}{x-a}$$

Dividing by x-a undoes the multiplication by x-a.

$$b=-\frac{ay}{x-a}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx}{y-b}\text{, }&b\neq y\\a\in \mathrm{R}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=y\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bx+ay-ab=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ay-ab=-bx$$

Combine all terms containing a.

$$\left(y-b\right)a=-bx$$

Divide both sides by y-b.

$$\frac{\left(y-b\right)a}{y-b}=-\frac{bx}{y-b}$$

Dividing by y-b undoes the multiplication by y-b.

$$a=-\frac{bx}{y-b}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ay}{x-a}\text{, }&x\neq a\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=a\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bx+ay-ab=0$$

Subtract ay from both sides. Anything subtracted from zero gives its negation.

$$bx-ab=-ay$$

Combine all terms containing b.

$$\left(x-a\right)b=-ay$$

Divide both sides by x-a.

$$\frac{\left(x-a\right)b}{x-a}=-\frac{ay}{x-a}$$

Dividing by x-a undoes the multiplication by x-a.

$$b=-\frac{ay}{x-a}$$