Chapter 11.10, Problem 50WE

To determine

To find: The solution set of the given system of equation.

Answer to Problem 50WE

The solution set is $\left\{8,18\right\}$ .

Explanation of Solution

Given:

The given system of equation are:

  $\begin{array}{c}5\sqrt{x}-2\sqrt{y}=4\sqrt{2}\dots \left(1\right)\\ 2\sqrt{x}+3\sqrt{y}=13\sqrt{2}\dots \left(2\right)\end{array}$

To find the solution of the given system, first, multiply equation $\left(1\right)$ by $3$ and equation $\left(2\right)$ by $2$ ,then add both the expression.

The calculation is given as:

  $\begin{array}{c}\left(15+4\right)\sqrt{x}+\left(6-6\right)\sqrt{y}=\left(12+26\right)\sqrt{2}\\ 19\sqrt{x}=38\sqrt{2}\\ \sqrt{x}=2\sqrt{2}\\ x=8\left[\text{squaring}\text{both}\text{side}\right]\end{array}$

Substitute $x=8$ in the equation $\left(1\right)$ ;

  $\begin{array}{c}5\sqrt{8}-2\sqrt{y}=4\sqrt{2}\\ 2\sqrt{y}=6\sqrt{2}\\ \sqrt{y}=3\sqrt{2}\\ y=18\left[\text{squaring}\text{both}\text{side}\right]\end{array}$

Therefore the solution set is $\left\{8,18\right\}$ .