Chapter 8.10, Problem 14PPS

(a)

To determine

The system of equations of:

The sum of two numbers is $5$ and the difference of the two numbers is $3$

Answer to Problem 14PPS

The system of equation is written as:

  $\begin{array}{l}x+y=5\\ x-y=3\end{array}$

Explanation of Solution

Given:

The sum of two numbers is $5$

The difference of the two numbers is $3$

Calculation:

Consider,

First number: $x$

Second number: $y$

The equations are written for given two problem conditions as:

  $x+y=5$....... (1)

  $x-y=3$....... (2)

Conclusion:

The system of equation is written as:

  $\begin{array}{l}x+y=5\\ x-y=3\end{array}$

(b)

To determine

The solution of the system by using the graphing method and meaning of the solution is to be needed.

Answer to Problem 14PPS

  

Explanation of Solution

Given:

The sum of two numbers is $5$

The difference of the two numbers is $3$

Calculation:

The equation is written as:

  $x+y=5$....... (1)

  $x-y=3$....... (2)

Now, draw a graph these two eqns.

  

From graph:

Notice that they have an intersection at $\left(3,0\right)$

This point is solution of the graphing eqns.

Conclusion:

So, by using the graphing method the solution of the system of equations is $\left(3,0\right)$ which is point of intersection.