Solve {c}{x+2y=5sqrt{5}}{sqrt{5}+y=5+2sqrt{5}}

$$\left. \begin{array} { c } { x + 2 y = 5 \sqrt { 5 } } \\ { \sqrt { 5 } + y = 5 + 2 \sqrt { 5 } } \end{array} \right.$$

Solve for x, y

$$x=3\sqrt{5}-10\approx -3.291796068$$

$$y=\sqrt{5}+5\approx 7.236067977$$

Solution Steps

Consider the second equation. Subtract \sqrt{5} from both sides.

$$y=5+2\sqrt{5}-\sqrt{5}$$

Combine 2\sqrt{5} and -\sqrt{5} to get \sqrt{5}.

$$y=5+\sqrt{5}$$

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

$$x+2\left(5+\sqrt{5}\right)=5\sqrt{5}$$

Use the distributive property to multiply 2 by 5+\sqrt{5}.

$$x+10+2\sqrt{5}=5\sqrt{5}$$

Subtract 10 from both sides.

$$x+2\sqrt{5}=5\sqrt{5}-10$$

Subtract 2\sqrt{5} from both sides.

$$x=5\sqrt{5}-10-2\sqrt{5}$$

Combine 5\sqrt{5} and -2\sqrt{5} to get 3\sqrt{5}.

$$x=3\sqrt{5}-10$$

The system is now solved.

$$x=3\sqrt{5}-10 y=5+\sqrt{5}$$