Solve 2bx-ay=ab

$$2 b x - a y = a b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2bx}{y+b}\text{, }&b\neq -y\\a\in \mathrm{C}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=-y\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$2bx-ay-ab=0$$

Subtract 2bx from both sides. Anything subtracted from zero gives its negation.

$$-ay-ab=-2bx$$

Combine all terms containing a.

$$\left(-y-b\right)a=-2bx$$

Divide both sides by -y-b.

$$\frac{\left(-y-b\right)a}{-y-b}=-\frac{2bx}{-y-b}$$

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

$$a=-\frac{2bx}{-y-b}$$

Divide -2bx by -y-b.

$$a=\frac{2bx}{y+b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{ay}{2x-a}\text{, }&x\neq \frac{a}{2}\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=\frac{a}{2}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$2bx-ay-ab=0$$

Add ay to both sides. Anything plus zero gives itself.

$$2bx-ab=ay$$

Combine all terms containing b.

$$\left(2x-a\right)b=ay$$

Divide both sides by 2x-a.

$$\frac{\left(2x-a\right)b}{2x-a}=\frac{ay}{2x-a}$$

Dividing by 2x-a undoes the multiplication by 2x-a.

$$b=\frac{ay}{2x-a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2bx}{y+b}\text{, }&b\neq -y\\a\in \mathrm{R}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=-y\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$2bx-ay-ab=0$$

Subtract 2bx from both sides. Anything subtracted from zero gives its negation.

$$-ay-ab=-2bx$$

Combine all terms containing a.

$$\left(-y-b\right)a=-2bx$$

Divide both sides by -y-b.

$$\frac{\left(-y-b\right)a}{-y-b}=-\frac{2bx}{-y-b}$$

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

$$a=-\frac{2bx}{-y-b}$$

Divide -2bx by -y-b.

$$a=\frac{2bx}{y+b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ay}{2x-a}\text{, }&x\neq \frac{a}{2}\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=\frac{a}{2}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$2bx-ay-ab=0$$

Add ay to both sides. Anything plus zero gives itself.

$$2bx-ab=ay$$

Combine all terms containing b.

$$\left(2x-a\right)b=ay$$

Divide both sides by 2x-a.

$$\frac{\left(2x-a\right)b}{2x-a}=\frac{ay}{2x-a}$$

Dividing by 2x-a undoes the multiplication by 2x-a.

$$b=\frac{ay}{2x-a}$$