Solve -I(10Omega)+6V-I(8Omega)-12V=0

$$- I ( 10 \Omega ) + 6 V - I ( 8 \Omega ) - 12 V = 0$$

Solve for I

$$\left\{\begin{matrix}I=-\frac{V}{3\Omega }\text{, }&\Omega \neq 0\\I\in \mathrm{R}\text{, }&V=0\text{ and }\Omega =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 12V to both sides. Anything plus zero gives itself.

$$\left(-I\right)\times 10\Omega +6V-I\times 8\Omega =12V$$

Multiply -1 and 10 to get -10.

$$-10I\Omega +6V-I\times 8\Omega =12V$$

Multiply -1 and 8 to get -8.

$$-10I\Omega +6V-8I\Omega =12V$$

Combine -10I\Omega and -8I\Omega to get -18I\Omega .

$$-18I\Omega +6V=12V$$

Subtract 6V from both sides.

$$-18I\Omega =12V-6V$$

Combine 12V and -6V to get 6V.

$$-18I\Omega =6V$$

The equation is in standard form.

$$\left(-18\Omega \right)I=6V$$

Divide both sides by -18\Omega .

$$\frac{\left(-18\Omega \right)I}{-18\Omega }=\frac{6V}{-18\Omega }$$

Dividing by -18\Omega undoes the multiplication by -18\Omega .

$$I=\frac{6V}{-18\Omega }$$

Divide 6V by -18\Omega .

$$I=-\frac{V}{3\Omega }$$

Solve for V

$$V=-3I\Omega$$

Steps for Solving Linear Equation

Multiply -1 and 10 to get -10.

$$-10I\Omega +6V-I\times 8\Omega -12V=0$$

Multiply -1 and 8 to get -8.

$$-10I\Omega +6V-8I\Omega -12V=0$$

Combine -10I\Omega and -8I\Omega to get -18I\Omega .

$$-18I\Omega +6V-12V=0$$

Combine 6V and -12V to get -6V.

$$-18I\Omega -6V=0$$

Add 18I\Omega to both sides. Anything plus zero gives itself.

$$-6V=18I\Omega$$

Divide both sides by -6.

$$\frac{-6V}{-6}=\frac{18I\Omega }{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$V=\frac{18I\Omega }{-6}$$

Divide 18I\Omega by -6.

$$V=-3I\Omega$$