Solve ax+1=bx-y

$$a x + 1 = b x - y$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$ax=bx-y-1$$

The equation is in standard form.

$$xa=bx-y-1$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{bx-y-1}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{bx-y-1}{x}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$bx-y=ax+1$$

Add y to both sides.

$$bx=ax+1+y$$

The equation is in standard form.

$$xb=ax+y+1$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ax+y+1}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ax+y+1}{x}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$ax=bx-y-1$$

The equation is in standard form.

$$xa=bx-y-1$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{bx-y-1}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{bx-y-1}{x}$$

Solve for b

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$bx-y=ax+1$$

Add y to both sides.

$$bx=ax+1+y$$

The equation is in standard form.

$$xb=ax+y+1$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ax+y+1}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ax+y+1}{x}$$