Solve y=bx+x

$$y = b x + x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$bx+x=y$$

Subtract x from both sides.

$$bx=y-x$$

The equation is in standard form.

$$xb=y-x$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{y-x}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide y-x by x.

$$b=\frac{y}{x}-1$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$bx+x=y$$

Combine all terms containing x.

$$\left(b+1\right)x=y$$

Divide both sides by b+1.

$$\frac{\left(b+1\right)x}{b+1}=\frac{y}{b+1}$$

Dividing by b+1 undoes the multiplication by b+1.

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

Solve for b

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

Steps for Solving Linear Equation

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

$$bx+x=y$$

Subtract x from both sides.

$$bx=y-x$$

The equation is in standard form.

$$xb=y-x$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{y-x}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide y-x by x.

$$b=\frac{y}{x}-1$$

Solve for x

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

Steps for Solving Linear Equation

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

$$bx+x=y$$

Combine all terms containing x.

$$\left(b+1\right)x=y$$

Divide both sides by b+1.

$$\frac{\left(b+1\right)x}{b+1}=\frac{y}{b+1}$$

Dividing by b+1 undoes the multiplication by b+1.

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