Chapter 3.5, Problem 33WE

To determine

To evaluate:Values of u and v using x and y.

Answer to Problem 33WE

The values of u and v are 2 and 3.

Explanation of Solution

Given information:

  $\frac{6}{u}$ + $\frac{3}{v}$=2

  $\frac{2}{u}$ - $\frac{\begin{array}{l}\\ 9\end{array}}{y}$ =4

Let,

  $x=\frac{1}{u},y=\frac{1}{v}$

Calculation:

Equations using x and y ,

  $6x+3y=2$ …(1)

  $2x-9y=4$ …(2)

On multiplying equation 1 by 3.

  $18x+9y=6$ ..(3)

On adding equation 2 and 3,

  $\begin{array}{l}2x+18x-(9y+9y)=6+4\\ 20x=10\\ x=\frac{1}{2}\end{array}$

Putting value of x in equation 2

  $\begin{array}{l}2\times (\frac{1}{2})-9y=4\\ 1-9y=4\\ -9y=4-1\\ -9y=-3\\ y=\frac{1}{3}\\ \end{array}$

The value of x and y is $\frac{1}{2}$ and $\frac{1}{3}$ .

According to question,

By using values of x and y ,

Value of u and v are 2 and 3.