#### Answer

The system of equations modeling the word problem is $x+y=7$ and $x-y=-1$ and the solution to the system of equations is $\left( x,y \right)=\left( 3,4 \right)$.

#### Work Step by Step

Let us assume the two numbers are x and y.
Sum of the numbers is 7. It gives the equation as:
$x+y=7$
And the difference between the numbers is −1. It gives the equation as:
$x-y=-1$
Add equations $x+y=7$ and $x-y=-1$ to obtain:
$\begin{align}
& x+y+x-y=7-1 \\
& 2x=6 \\
& x=3
\end{align}$
Put the value of x in the equation $x+y=7$ to obtain:
$\begin{align}
& 3+y=7 \\
& y=4
\end{align}$
Hence, thee systems of equations is $x+y=7$ and $x-y=-1$ and the solution of the equations is $\left( x,y \right)=\left( 3,4 \right)$.