Solve z=ax+by

$$z = a x + b y$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax+by=z$$

Subtract by from both sides.

$$ax=z-by$$

The equation is in standard form.

$$xa=z-by$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Solve for b

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

Steps for Solving Linear Equation

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

$$ax+by=z$$

Subtract ax from both sides.

$$by=z-ax$$

The equation is in standard form.

$$yb=z-ax$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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