Chapter 8.1, Problem 18WE

To determine

To find: The solution of the given equation.

Answer to Problem 18WE

The solutions are $\left(0,3\right)$ , $\left(3,2\right)$ , $\left(6,1\right)$ and $\left(9,0\right)$ .

Explanation of Solution

Given:

The given equation is:

  $x+3y=9$

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

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

  $\begin{array}{l}3y=9-x\\ y=\frac{9-x}{3}\end{array}$

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

Table1

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

As, values of $x$ greater than $9$ gives negative fractional values of $y$ .

Therefore, the solutions are $\left(0,3\right)$ , $\left(3,2\right)$ , $\left(6,1\right)$ and $\left(9,0\right)$ .