Solve a_{21}x_{1}+a_{22}x_{2}=b_{2}

$$a _ { 21 } x _ { 1 } + a _ { 22 } x _ { 2 } = b _ { 2 }$$

Solve for a_21

$$\left\{\begin{matrix}a_{21}=-\frac{a_{22}x_{2}-b_{2}}{x_{1}}\text{, }&x_{1}\neq 0\\a_{21}\in \mathrm{R}\text{, }&b_{2}=a_{22}x_{2}\text{ and }x_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{22}x_{2} from both sides.

$$a_{21}x_{1}=b_{2}-a_{22}x_{2}$$

The equation is in standard form.

$$x_{1}a_{21}=b_{2}-a_{22}x_{2}$$

Divide both sides by x_{1}.

$$\frac{x_{1}a_{21}}{x_{1}}=\frac{b_{2}-a_{22}x_{2}}{x_{1}}$$

Dividing by x_{1} undoes the multiplication by x_{1}.

$$a_{21}=\frac{b_{2}-a_{22}x_{2}}{x_{1}}$$

Solve for a_22

$$\left\{\begin{matrix}a_{22}=-\frac{a_{21}x_{1}-b_{2}}{x_{2}}\text{, }&x_{2}\neq 0\\a_{22}\in \mathrm{R}\text{, }&b_{2}=a_{21}x_{1}\text{ and }x_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{21}x_{1} from both sides.

$$a_{22}x_{2}=b_{2}-a_{21}x_{1}$$

The equation is in standard form.

$$x_{2}a_{22}=b_{2}-a_{21}x_{1}$$

Divide both sides by x_{2}.

$$\frac{x_{2}a_{22}}{x_{2}}=\frac{b_{2}-a_{21}x_{1}}{x_{2}}$$

Dividing by x_{2} undoes the multiplication by x_{2}.

$$a_{22}=\frac{b_{2}-a_{21}x_{1}}{x_{2}}$$