Solve {c}{U-frac{UR_{x}}{R_{x}+100}-U/2=10^-3}{U=3}

$$\left. \begin{array} { c } { U - \frac { U R _ { x } } { R _ { x } + 100 } - \frac { U } { 2 } = 10 ^ { - 3 } } \\ { U = 3 } \end{array} \right.$$

Solve for U, R_x

$$U=3$$

$$R_{x} = \frac{149900}{1501} = 99\frac{1301}{1501} \approx 99.866755496$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$3-\frac{3R_{x}}{R_{x}+100}-\frac{3}{2}=10^{-3}$$

Variable R_{x} cannot be equal to -100 since division by zero is not defined. Multiply both sides of the equation by 2\left(R_{x}+100\right), the least common multiple of R_{x}+100,2.

$$2\left(R_{x}+100\right)\times 3-2\times 3R_{x}-\left(R_{x}+100\right)\times 3=2\left(R_{x}+100\right)\times 10^{-3}$$

Use the distributive property to multiply 2 by R_{x}+100.

$$\left(2R_{x}+200\right)\times 3-2\times 3R_{x}-\left(R_{x}+100\right)\times 3=2\left(R_{x}+100\right)\times 10^{-3}$$

Use the distributive property to multiply 2R_{x}+200 by 3.

$$6R_{x}+600-2\times 3R_{x}-\left(R_{x}+100\right)\times 3=2\left(R_{x}+100\right)\times 10^{-3}$$

Multiply -2 and 3 to get -6.

$$6R_{x}+600-6R_{x}-\left(R_{x}+100\right)\times 3=2\left(R_{x}+100\right)\times 10^{-3}$$

Combine 6R_{x} and -6R_{x} to get 0.

$$600-\left(R_{x}+100\right)\times 3=2\left(R_{x}+100\right)\times 10^{-3}$$

Use the distributive property to multiply R_{x}+100 by 3.

$$600-\left(3R_{x}+300\right)=2\left(R_{x}+100\right)\times 10^{-3}$$

To find the opposite of 3R_{x}+300, find the opposite of each term.

$$600-3R_{x}-300=2\left(R_{x}+100\right)\times 10^{-3}$$

Subtract 300 from 600 to get 300.

$$300-3R_{x}=2\left(R_{x}+100\right)\times 10^{-3}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$300-3R_{x}=2\left(R_{x}+100\right)\times \frac{1}{1000}$$

Multiply 2 and \frac{1}{1000} to get \frac{1}{500}.

$$300-3R_{x}=\frac{1}{500}\left(R_{x}+100\right)$$

Use the distributive property to multiply \frac{1}{500} by R_{x}+100.

$$300-3R_{x}=\frac{1}{500}R_{x}+\frac{1}{5}$$

Subtract \frac{1}{500}R_{x} from both sides.

$$300-3R_{x}-\frac{1}{500}R_{x}=\frac{1}{5}$$

Combine -3R_{x} and -\frac{1}{500}R_{x} to get -\frac{1501}{500}R_{x}.

$$300-\frac{1501}{500}R_{x}=\frac{1}{5}$$

Subtract 300 from both sides.

$$-\frac{1501}{500}R_{x}=\frac{1}{5}-300$$

Subtract 300 from \frac{1}{5} to get -\frac{1499}{5}.

$$-\frac{1501}{500}R_{x}=-\frac{1499}{5}$$

Multiply both sides by -\frac{500}{1501}, the reciprocal of -\frac{1501}{500}.

$$R_{x}=-\frac{1499}{5}\left(-\frac{500}{1501}\right)$$

Multiply -\frac{1499}{5} and -\frac{500}{1501} to get \frac{149900}{1501}.

$$R_{x}=\frac{149900}{1501}$$

The system is now solved.

$$U=3 R_{x}=\frac{149900}{1501}$$