Solve {c}{y=14k/k^2+1}{k=2/7}

$$\left. \begin{array} { c } { y = \frac { 14 k } { k ^ { 2 } + 1 } } \\ { k = \frac { 2 } { 7 } } \end{array} \right.$$

Solve for y, k

$$y = \frac{196}{53} = 3\frac{37}{53} \approx 3.698113208$$

$$k=\frac{2}{7}\approx 0.285714286$$

Solution Steps

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

$$y=\frac{14\times \frac{2}{7}}{\left(\frac{2}{7}\right)^{2}+1}$$

Multiply 14 and \frac{2}{7} to get 4.

$$y=\frac{4}{\left(\frac{2}{7}\right)^{2}+1}$$

Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.

$$y=\frac{4}{\frac{4}{49}+1}$$

Add \frac{4}{49} and 1 to get \frac{53}{49}.

$$y=\frac{4}{\frac{53}{49}}$$

Divide 4 by \frac{53}{49} by multiplying 4 by the reciprocal of \frac{53}{49}.

$$y=4\times \frac{49}{53}$$

Multiply 4 and \frac{49}{53} to get \frac{196}{53}.

$$y=\frac{196}{53}$$

The system is now solved.

$$y=\frac{196}{53} k=\frac{2}{7}$$