Solve x+y+ixy=i

$$x + y + i x y = i$$

Solve for x

$$\left\{\begin{matrix}x=i\text{, }&y\neq i\\x\in \mathrm{C}\text{, }&y=i\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$x+ixy=i-y$$

Combine all terms containing x.

$$\left(1+iy\right)x=i-y$$

The equation is in standard form.

$$\left(iy+1\right)x=i-y$$

Divide both sides by 1+iy.

$$\frac{\left(iy+1\right)x}{iy+1}=\frac{i-y}{iy+1}$$

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

$$x=\frac{i-y}{iy+1}$$

Divide i-y by 1+iy.

$$x=i$$

Solve for y

$$\left\{\begin{matrix}y=i\text{, }&x\neq i\\y\in \mathrm{C}\text{, }&x=i\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$y+ixy=i-x$$

Combine all terms containing y.

$$\left(1+ix\right)y=i-x$$

The equation is in standard form.

$$\left(ix+1\right)y=i-x$$

Divide both sides by 1+ix.

$$\frac{\left(ix+1\right)y}{ix+1}=\frac{i-x}{ix+1}$$

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

$$y=\frac{i-x}{ix+1}$$

Divide i-x by 1+ix.

$$y=i$$