Solve a1*b1=a2*b2

$$a 1 \cdot b 1 = a 2 \cdot b 2$$

Solve for a_1 (complex solution)

$$\left\{\begin{matrix}a_{1}=\frac{a_{2}b_{2}}{b_{1}}\text{, }&b_{1}\neq 0\\a_{1}\in \mathrm{C}\text{, }&\left(a_{2}=0\text{ or }b_{2}=0\right)\text{ and }b_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$b_{1}a_{1}=a_{2}b_{2}$$

Divide both sides by b_{1}.

$$\frac{b_{1}a_{1}}{b_{1}}=\frac{a_{2}b_{2}}{b_{1}}$$

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

$$a_{1}=\frac{a_{2}b_{2}}{b_{1}}$$

Solve for a_2 (complex solution)

$$\left\{\begin{matrix}a_{2}=\frac{a_{1}b_{1}}{b_{2}}\text{, }&b_{2}\neq 0\\a_{2}\in \mathrm{C}\text{, }&\left(a_{1}=0\text{ or }b_{1}=0\right)\text{ and }b_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a_{2}b_{2}=a_{1}b_{1}$$

The equation is in standard form.

$$b_{2}a_{2}=a_{1}b_{1}$$

Divide both sides by b_{2}.

$$\frac{b_{2}a_{2}}{b_{2}}=\frac{a_{1}b_{1}}{b_{2}}$$

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

$$a_{2}=\frac{a_{1}b_{1}}{b_{2}}$$

Solve for a_1

$$\left\{\begin{matrix}a_{1}=\frac{a_{2}b_{2}}{b_{1}}\text{, }&b_{1}\neq 0\\a_{1}\in \mathrm{R}\text{, }&\left(a_{2}=0\text{ or }b_{2}=0\right)\text{ and }b_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$b_{1}a_{1}=a_{2}b_{2}$$

Divide both sides by b_{1}.

$$\frac{b_{1}a_{1}}{b_{1}}=\frac{a_{2}b_{2}}{b_{1}}$$

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

$$a_{1}=\frac{a_{2}b_{2}}{b_{1}}$$

Solve for a_2

$$\left\{\begin{matrix}a_{2}=\frac{a_{1}b_{1}}{b_{2}}\text{, }&b_{2}\neq 0\\a_{2}\in \mathrm{R}\text{, }&\left(a_{1}=0\text{ or }b_{1}=0\right)\text{ and }b_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a_{2}b_{2}=a_{1}b_{1}$$

The equation is in standard form.

$$b_{2}a_{2}=a_{1}b_{1}$$

Divide both sides by b_{2}.

$$\frac{b_{2}a_{2}}{b_{2}}=\frac{a_{1}b_{1}}{b_{2}}$$

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

$$a_{2}=\frac{a_{1}b_{1}}{b_{2}}$$