Solve RQ=Q_{3}-Q_{1}

$$R Q = Q _ { 3 } - Q _ { 1 }$$

Solve for Q

$$\left\{\begin{matrix}Q=-\frac{Q_{1}-Q_{3}}{R}\text{, }&R\neq 0\\Q\in \mathrm{R}\text{, }&Q_{3}=Q_{1}\text{ and }R=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$RQ=Q_{3}-Q_{1}$$

Divide both sides by R.

$$\frac{RQ}{R}=\frac{Q_{3}-Q_{1}}{R}$$

Dividing by R undoes the multiplication by R.

$$Q=\frac{Q_{3}-Q_{1}}{R}$$

Solve for Q_1

$$Q_{1}=Q_{3}-QR$$

Steps for Solving Linear Equation

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

$$Q_{3}-Q_{1}=RQ$$

Subtract Q_{3} from both sides.

$$-Q_{1}=RQ-Q_{3}$$

The equation is in standard form.

$$-Q_{1}=QR-Q_{3}$$

Divide both sides by -1.

$$\frac{-Q_{1}}{-1}=\frac{QR-Q_{3}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$Q_{1}=\frac{QR-Q_{3}}{-1}$$

Divide QR-Q_{3} by -1.

$$Q_{1}=Q_{3}-QR$$