Solve a_{j}x+a_{2}y=b_{1}

$$a _ { j } x + a _ { 2 } y = b _ { 1 }$$

Solve for a_2 (complex solution)

$$\left\{\begin{matrix}a_{2}=-\frac{a_{j}x-b_{1}}{y}\text{, }&y\neq 0\\a_{2}\in \mathrm{C}\text{, }&b_{1}=a_{j}x\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{j}x from both sides.

$$a_{2}y=b_{1}-a_{j}x$$

The equation is in standard form.

$$ya_{2}=b_{1}-a_{j}x$$

Divide both sides by y.

$$\frac{ya_{2}}{y}=\frac{b_{1}-a_{j}x}{y}$$

Dividing by y undoes the multiplication by y.

$$a_{2}=\frac{b_{1}-a_{j}x}{y}$$

Solve for a_j (complex solution)

$$\left\{\begin{matrix}a_{j}=-\frac{a_{2}y-b_{1}}{x}\text{, }&x\neq 0\\a_{j}\in \mathrm{C}\text{, }&b_{1}=a_{2}y\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{2}y from both sides.

$$a_{j}x=b_{1}-a_{2}y$$

The equation is in standard form.

$$xa_{j}=b_{1}-a_{2}y$$

Divide both sides by x.

$$\frac{xa_{j}}{x}=\frac{b_{1}-a_{2}y}{x}$$

Dividing by x undoes the multiplication by x.

$$a_{j}=\frac{b_{1}-a_{2}y}{x}$$

Solve for a_2

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

Steps for Solving Linear Equation

Subtract a_{j}x from both sides.

$$a_{2}y=b_{1}-a_{j}x$$

The equation is in standard form.

$$ya_{2}=b_{1}-a_{j}x$$

Divide both sides by y.

$$\frac{ya_{2}}{y}=\frac{b_{1}-a_{j}x}{y}$$

Dividing by y undoes the multiplication by y.

$$a_{2}=\frac{b_{1}-a_{j}x}{y}$$

Solve for a_j

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

Steps for Solving Linear Equation

Subtract a_{2}y from both sides.

$$a_{j}x=b_{1}-a_{2}y$$

The equation is in standard form.

$$xa_{j}=b_{1}-a_{2}y$$

Divide both sides by x.

$$\frac{xa_{j}}{x}=\frac{b_{1}-a_{2}y}{x}$$

Dividing by x undoes the multiplication by x.

$$a_{j}=\frac{b_{1}-a_{2}y}{x}$$