Chapter 8.1, Problem 16WE

To determine

To find: The solution of the given equation.

Answer to Problem 16WE

The solutions are $\left(0,2\right)$ and $\left(5,0\right)$ .

Explanation of Solution

Given:

The given equation is:

  $2x+5y=10$

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

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

  $\begin{array}{l}5y=10-2x\\ y=\frac{10-2x}{5}\end{array}$

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

Table1

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

As, values of $x$ greater than $5$ gives negative fractional values of $y$ .

Therefore, the solutions are $\left(0,2\right)$ and $\left(5,0\right)$ .