#### Answer

The equations modeling the word problem are $3x+2y=8\text{ and }2x-y=3$ and the solution to the system of equations is $\left( x,y \right)=\left( 2,1 \right)$.

#### Work Step by Step

Let us assume the first number is x and the second number is y.
And addition of three times the first number with twice the second number gives 8. This can be represented by the equation:
$3x+2y=8$
And subtraction of the second number from two times the first number gives 3. This can be represented by the equation:
$2x-y=3$
And multiply equation $2x-y=3$ by 2 to obtain:
$4x-2y=6$
And add equations $3x+2y=8$ and $2x-y=3$:
$\begin{align}
& 3x+2y+4x-2y=8+6 \\
& 7x=14 \\
& x=2
\end{align}$
Put the value $x=2$ in the equation $3x+2y=8$:
$\begin{align}
& 6+2y=8 \\
& 2y=2 \\
& y=1
\end{align}$
Thus, the equations modeling the word problem are $3x+2y=8\text{ and }2x-y=3$ and the solution to the system of equations is $\left( x,y \right)=\left( 2,1 \right)$.