Solve {l}{y^2=5/2x}{y=5/2sqrt{3}}

$$\left. \begin{array} { l } { y ^ { 2 } = \frac { 5 } { 2 } x } \\ { y = \frac { 5 } { 2 } \sqrt { 3 } } \end{array} \right.$$

Solve for y, x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$y = \frac{5 \sqrt{3}}{2} \approx 4.330127019$$

Solution Steps

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

$$\left(\frac{5}{2}\sqrt{3}\right)^{2}=\frac{5}{2}x$$

Expand \left(\frac{5}{2}\sqrt{3}\right)^{2}.

$$\left(\frac{5}{2}\right)^{2}\left(\sqrt{3}\right)^{2}=\frac{5}{2}x$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}\left(\sqrt{3}\right)^{2}=\frac{5}{2}x$$

The square of \sqrt{3} is 3.

$$\frac{25}{4}\times 3=\frac{5}{2}x$$

Multiply \frac{25}{4} and 3 to get \frac{75}{4}.

$$\frac{75}{4}=\frac{5}{2}x$$

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

$$\frac{5}{2}x=\frac{75}{4}$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$x=\frac{75}{4}\times \frac{2}{5}$$

Multiply \frac{75}{4} and \frac{2}{5} to get \frac{15}{2}.

$$x=\frac{15}{2}$$

The system is now solved.

$$y=\frac{5}{2}\sqrt{3} x=\frac{15}{2}$$