Chapter 9, Problem 33CR

To determine

To write a system of equations and solve the system to find the numbers.

Answer to Problem 33CR

The system of equations can be written as:

  $\begin{array}{l}\text{x}+\text{y}=\text{9}\\ \text{x}-\text{y}=\text{1}\end{array}$

The solution of the system of equations is $\left(5,4\right)$ .

Explanation of Solution

Given information:

The given statement is:

“The sum of two numbers is $\text{9}$ , and the difference of the numbers is $\text{1}$ .”

Calculation :

The system of equations can be written as:

  $\begin{array}{l}\text{x}+\text{y}=\text{9}\\ \text{x}-\text{y}=\text{1}\end{array}$

The graph of the equations are:

The graph is intersecting at $\left(5,4\right)$ .

Check by substituting the values of $\text{x and y}$ by $\left(5,4\right)$ :

  $\begin{array}{l}\text{x}+\text{y}=\text{9}\\ 5+4=9\\ 9=9\\ \\ \text{x}-\text{y}=\text{1}\\ 5-4=1\\ 1=1\end{array}$

Hence, the solution of the system of equations is $\left(5,4\right)$ .