Chapter 11.1, Problem 39AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 39AYU

Solution:

  $x=\frac{1}{5},y=\frac{1}{3}$

Explanation of Solution

Given:

  $\frac{1}{x}+\frac{1}{y}=8$

  $\frac{3}{x}-\frac{5}{y}=0$

Calculation:

The system of equations is:

  $\frac{1}{x}+\frac{1}{y}=8$

  $\frac{3}{x}-\frac{5}{y}=0$

From the second equation we get,

  $\frac{2}{x}=\frac{5}{y}$

  $\frac{1}{x}=\frac{5}{3y}$

Substituting $\frac{1}{x}=\frac{5}{3y}$ in the first equation we get,

  $\frac{5}{2y}+\frac{1}{y}=8$

  $\frac{8}{3y}=8$

  $y=\frac{1}{3}$

Substituting $y=\frac{1}{3}$ in the first equation we get,

  $\frac{1}{x}+\frac{1}{\frac{1}{3}}=8$

  $\frac{1}{x}+3=8$

  $\frac{1}{x}=8-3$

  $\frac{1}{x}=5$

  $x=\frac{1}{5}$

Thus $x=\frac{1}{5},y=\frac{1}{3}$ is the solution of the given system of equations.