Chapter 8.1, Problem 14OE

To determine

To solve: The given equation if x and y are whole numbers.

Answer to Problem 14OE

The solution is $\left(1,3\right)$ , $\left(3,2\right)$ , $\left(5,1\right)$ and $\left(7,0\right)$ .

Explanation of Solution

Given:

The equation is $x+2y=7$ .

Calculation:

Determine the equation in terms of x , as shown below:

  $\begin{array}{c}x+2y=7\\ x+2y-x=7-x\left[\text{Subtracting }x\text{ from both sides}\right]\\ 2y=7-x\\ y=\frac{7-x}{2}\left[\text{Dividing both sides by }2\right]\end{array}$

In order to solve the equation, substitute different values of x , starting from 0, to obtain the respective values of y that satisfy the equation.

For $x=0$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-0}{2}\\ =\frac{7}{2}\ne \text{whole number}\end{array}$

For $x=1$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-1}{2}\\ =\frac{6}{2}\\ =3\end{array}$

For $x=2$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-2}{2}\\ =\frac{5}{2}\ne \text{whole number}\end{array}$

For $x=3$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-3}{2}\\ =\frac{4}{2}\\ =2\end{array}$

For $x=4$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-4}{2}\\ =\frac{3}{2}\ne \text{whole number}\end{array}$

For $x=5$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-5}{2}\\ =\frac{2}{2}\\ =1\end{array}$

For $x=6$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-6}{2}\\ =\frac{1}{2}\ne \text{whole number}\end{array}$

For $x=7$ ,

  $\begin{array}{c}y=\frac{7-x}{2}\\ =\frac{7-7}{2}\\ =\frac{0}{2}\\ =0\end{array}$

Since both x and y are whole numbers, the solution of the equation becomes $\left(1,3\right)$ , $\left(3,2\right)$ , $\left(5,1\right)$ and $\left(7,0\right)$ .