Solve x+a=xy

$$x + a = x y$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract xy from both sides.

$$x+a-xy=0$$

Subtract a from both sides. Anything subtracted from zero gives its negation.

$$x-xy=-a$$

Combine all terms containing x.

$$\left(1-y\right)x=-a$$

Divide both sides by 1-y.

$$\frac{\left(1-y\right)x}{1-y}=-\frac{a}{1-y}$$

Dividing by 1-y undoes the multiplication by 1-y.

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

Solve for x

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

Steps for Solving Linear Equation

Subtract xy from both sides.

$$x+a-xy=0$$

Subtract a from both sides. Anything subtracted from zero gives its negation.

$$x-xy=-a$$

Combine all terms containing x.

$$\left(1-y\right)x=-a$$

Divide both sides by 1-y.

$$\frac{\left(1-y\right)x}{1-y}=-\frac{a}{1-y}$$

Dividing by 1-y undoes the multiplication by 1-y.

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

Solve for a

$$a=x\left(y-1\right)$$

Solution Steps

Subtract x from both sides.

$$a=xy-x$$