Solve ar_{1}=a(1-e)

$$a r _ { 1 } = a ( 1 - e )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&r_{1}=1-e\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-e.

$$ar_{1}=a-ae$$

Subtract a from both sides.

$$ar_{1}-a=-ae$$

Add ae to both sides.

$$ar_{1}-a+ae=0$$

Combine all terms containing a.

$$\left(r_{1}-1+e\right)a=0$$

The equation is in standard form.

$$\left(r_{1}+e-1\right)a=0$$

Divide 0 by r_{1}-1+e.

$$a=0$$

Solve for r_1 (complex solution)

$$\left\{\begin{matrix}\\r_{1}=1-e\text{, }&\text{unconditionally}\\r_{1}\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-e.

$$ar_{1}=a-ae$$

The equation is in standard form.

$$ar_{1}=a-ea$$

Divide both sides by a.

$$\frac{ar_{1}}{a}=\frac{a-ea}{a}$$

Dividing by a undoes the multiplication by a.

$$r_{1}=\frac{a-ea}{a}$$

Divide a-ae by a.

$$r_{1}=1-e$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&r_{1}=1-e\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-e.

$$ar_{1}=a-ae$$

Subtract a from both sides.

$$ar_{1}-a=-ae$$

Add ae to both sides.

$$ar_{1}-a+ae=0$$

Combine all terms containing a.

$$\left(r_{1}-1+e\right)a=0$$

The equation is in standard form.

$$\left(r_{1}+e-1\right)a=0$$

Divide 0 by r_{1}-1+e.

$$a=0$$

Solve for r_1

$$\left\{\begin{matrix}\\r_{1}=1-e\text{, }&\text{unconditionally}\\r_{1}\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-e.

$$ar_{1}=a-ae$$

The equation is in standard form.

$$ar_{1}=a-ea$$

Divide both sides by a.

$$\frac{ar_{1}}{a}=\frac{a-ea}{a}$$

Dividing by a undoes the multiplication by a.

$$r_{1}=\frac{a-ea}{a}$$

Divide a-ae by a.

$$r_{1}=1-e$$