Solve {l}{y^2=5x}{y=5/4sqrt{3}}

$$\left. \begin{array} { l } { y ^ { 2 } = 5 x } \\ { y = \frac { 5 } { 4 } \sqrt { 3 } } \end{array} \right.$$

Solve for y, x

$$x=\frac{15}{16}=0.9375$$

$$y = \frac{5 \sqrt{3}}{4} \approx 2.165063509$$

Solution Steps

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

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

Expand \left(\frac{5}{4}\sqrt{3}\right)^{2}.

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

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{25}{16}\left(\sqrt{3}\right)^{2}=5x$$

The square of \sqrt{3} is 3.

$$\frac{25}{16}\times 3=5x$$

Multiply \frac{25}{16} and 3 to get \frac{75}{16}.

$$\frac{75}{16}=5x$$

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

$$5x=\frac{75}{16}$$

Divide both sides by 5.

$$x=\frac{\frac{75}{16}}{5}$$

Express \frac{\frac{75}{16}}{5} as a single fraction.

$$x=\frac{75}{16\times 5}$$

Multiply 16 and 5 to get 80.

$$x=\frac{75}{80}$$

Reduce the fraction \frac{75}{80} to lowest terms by extracting and canceling out 5.

$$x=\frac{15}{16}$$

The system is now solved.

$$y=\frac{5}{4}\sqrt{3} x=\frac{15}{16}$$