Solve varepsilon=x+ay,eta

$$\varepsilon = x + a y , \eta$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$x+ay=\epsilon$$

Subtract x from both sides.

$$ay=\epsilon -x$$

The equation is in standard form.

$$ya=\epsilon -x$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{\epsilon -x}{y}$$

Dividing by y undoes the multiplication by y.

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

Solve for a

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

Steps for Solving Linear Equation

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

$$x+ay=\epsilon$$

Subtract x from both sides.

$$ay=\epsilon -x$$

The equation is in standard form.

$$ya=\epsilon -x$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{\epsilon -x}{y}$$

Dividing by y undoes the multiplication by y.

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

Solve for x

$$x=\epsilon -ay$$

Solution Steps

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

$$x+ay=\epsilon$$

Subtract ay from both sides.

$$x=\epsilon -ay$$