Solve {l}{lambda=2Vm/1-2V}{m=7.54}{lambda=12.14}{z=2*7.54/16.84-12.14}

$$\left. \begin{array} { l } { \lambda = \frac { 2 V m } { 1 - 2 V } } \\ { m = 7.54 } \\ { \lambda = 12.14 } \\ { z = \frac { 2 \times 7.54 } { 16.84 - 12.14 } } \end{array} \right.$$

Solve for λ, V, m, z

$$z = \frac{754}{235} = 3\frac{49}{235} \approx 3.208510638$$

$$\lambda =12.14$$

$$V=\frac{607}{1968}\approx 0.308434959$$

$$m=7.54$$

Solution Steps

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

$$12.14=\frac{2V\times 7.54}{1-2V}$$

Variable V cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by -2V+1.

$$12.14\left(-2V+1\right)=2V\times 7.54$$

Use the distributive property to multiply 12.14 by -2V+1.

$$-24.28V+12.14=2V\times 7.54$$

Multiply 2 and 7.54 to get 15.08.

$$-24.28V+12.14=15.08V$$

Subtract 15.08V from both sides.

$$-24.28V+12.14-15.08V=0$$

Combine -24.28V and -15.08V to get -39.36V.

$$-39.36V+12.14=0$$

Subtract 12.14 from both sides. Anything subtracted from zero gives its negation.

$$-39.36V=-12.14$$

Divide both sides by -39.36.

$$V=\frac{-12.14}{-39.36}$$

Expand \frac{-12.14}{-39.36} by multiplying both numerator and the denominator by 100.

$$V=\frac{-1214}{-3936}$$

Reduce the fraction \frac{-1214}{-3936} to lowest terms by extracting and canceling out -2.

$$V=\frac{607}{1968}$$

Consider the fourth equation. Multiply 2 and 7.54 to get 15.08.

$$z=\frac{15.08}{16.84-12.14}$$

Subtract 12.14 from 16.84 to get 4.7.

$$z=\frac{15.08}{4.7}$$

Expand \frac{15.08}{4.7} by multiplying both numerator and the denominator by 100.

$$z=\frac{1508}{470}$$

Reduce the fraction \frac{1508}{470} to lowest terms by extracting and canceling out 2.

$$z=\frac{754}{235}$$

The system is now solved.

$$\lambda =12.14 V=\frac{607}{1968} m=7.54 z=\frac{754}{235}$$