Q17. - Algebra 1

Question

Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two variables, write a system of equations, and solve by graphing.

Step-by-Step Solution

Answer

The graph of the system of equations:-

$\begin{array}{l}x+y=14\\ x-y=4\end{array}$

The solution of the system of equations is $\left(9,5\right)$.

Step 1. Write a system of equations.

To write a system of equations consider: 

First variable: x

Second variable: y

 

As per the condition given in the problem: 

 

Case 1: Sum of two variables is 14.

$x+y=14$                                             … (1)

 

Case 2: Difference of two variables is $4$

$x-y=4$                                              … (2)

Step 2. Graph the system of equations.

The graph of two equations is drawn as below.

Step 3. Interpret the system of equations and graph.

Now the intersection point of two straight lines shown by equations (1) and (2) is $\left(9,5\right)$.

This intersection point of two lines is nothing but the solution set of given system of equation.

Therefore, one solution of given system of equation is labelled as $\left(9,5\right)$.