Chapter 8.1, Problem 22WE

To determine

To find: The solution of the given equation.

Answer to Problem 22WE

The solutions are $\left(1,12\right)$ , $\left(2,6\right)$ , $\left(3,4\right)$ , $\left(4,3\right)$ and $\left(12,1\right)$ .

Explanation of Solution

Given:

The given equation is:

  $xy=12$

Here, $x$ and $y$ are the whole numbers.

Solve the given equation for $y$ in terms of $x$ .

  $y=\frac{12}{x}$

The table given below shows the corresponding value of $y$ after replacing $x$ with successive whole numbers is as:

Table1

$x$	$y=\frac{4}{x}$	Solution
$0$	$\frac{12}{0}=\infty$	No solution
$1$	$\frac{12}{1}=12$	$\left(1,12\right)$
$2$	$\frac{12}{2}=6$	$\left(2,6\right)$
$3$	$\frac{12}{3}=4$	$\left(3,4\right)$
$4$	$$ $\frac{12}{4}=3$	$\left(4,3\right)$
$5$	$\frac{12}{5}$	No solution
$6$	$\frac{12}{6}=2$	$\left(6,2\right)$
$7$	$\frac{12}{7}$	No solution
$8$	$\frac{12}{8}$	No solution
$9$	$\frac{12}{9}$	No solution
$10$	$\frac{12}{10}$	No solution
$11$	$\frac{12}{11}$	No solution
$12$	$\frac{12}{12}=1$	$\left(12,1\right)$

As, it is given $x$ and $y$ are the whole numbers and values of $x$ greater than $12$ gives fractional values of $y$ .

Therefore, the solutions are $\left(1,12\right)$ , $\left(2,6\right)$ , $\left(3,4\right)$ , $\left(4,3\right)$ and $\left(12,1\right)$ .