Solve -2+ax+by=-x-y

$$-2+ax+by = -x-y$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x+by+y-2}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=-1+\frac{2}{y}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$ax+by=-x-y+2$$

Subtract by from both sides.

$$ax=-x-y+2-by$$

The equation is in standard form.

$$xa=2-y-by-x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{2-y-by-x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{2-y-by-x}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ax+x+y-2}{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&y=0\text{ and }a=-1+\frac{2}{x}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$ax+by=-x-y+2$$

Subtract ax from both sides.

$$by=-x-y+2-ax$$

The equation is in standard form.

$$yb=2-y-x-ax$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{2-y-x-ax}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{2-y-x-ax}{y}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x+by+y-2}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=-1+\frac{2}{y}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$ax+by=-x-y+2$$

Subtract by from both sides.

$$ax=-x-y+2-by$$

The equation is in standard form.

$$xa=2-y-by-x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{2-y-by-x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{2-y-by-x}{x}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax+x+y-2}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&y=0\text{ and }a=-1+\frac{2}{x}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$ax+by=-x-y+2$$

Subtract ax from both sides.

$$by=-x-y+2-ax$$

The equation is in standard form.

$$yb=2-y-x-ax$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{2-y-x-ax}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{2-y-x-ax}{y}$$