Solve U=E-I*R_{s}

$$U = E - I \cdot R _ { s }$$

Solve for E

$$E=IR_{s}+U$$

Solution Steps

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

$$E-IR_{s}=U$$

Add IR_{s} to both sides.

$$E=U+IR_{s}$$

Solve for I

$$\left\{\begin{matrix}I=\frac{E-U}{R_{s}}\text{, }&R_{s}\neq 0\\I\in \mathrm{R}\text{, }&U=E\text{ and }R_{s}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$E-IR_{s}=U$$

Subtract E from both sides.

$$-IR_{s}=U-E$$

The equation is in standard form.

$$\left(-R_{s}\right)I=U-E$$

Divide both sides by -R_{s}.

$$\frac{\left(-R_{s}\right)I}{-R_{s}}=\frac{U-E}{-R_{s}}$$

Dividing by -R_{s} undoes the multiplication by -R_{s}.

$$I=\frac{U-E}{-R_{s}}$$

Divide U-E by -R_{s}.

$$I=-\frac{U-E}{R_{s}}$$