Solve z=ax+y

$$z = a x + y$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax+y=z$$

Subtract y from both sides.

$$ax=z-y$$

The equation is in standard form.

$$xa=z-y$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{z-y}{x}$$

Dividing by x undoes the multiplication by x.

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

Solve for x

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

Steps for Solving Linear Equation

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

$$ax+y=z$$

Subtract y from both sides.

$$ax=z-y$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{z-y}{a}$$

Dividing by a undoes the multiplication by a.

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