#### Answer

The system of equations are $3x-y=1$ and $x+2y=12$. Solution of the equations is $\left( x,y \right)=\left( 2,5 \right)$.

#### Work Step by Step

Let us assume the first number is x and the second number is y.
Subtract the second number from three times the first number to get 1. This gives the equation as:
$3x-y=1$
And addition of the first number and twice the second number gives 12. This gives the equation as:
$x+2y=12$
Multiply the equation $3x-y=1$ by 2
$6x-2y=2$
And add equations $x+2y=12$ and $6x-2y=2$ to obtain:
$\begin{align}
& x+2y+6x-2y=12+2 \\
& 7x=14 \\
& x=2
\end{align}$
Put the value of x in the equation $3x-y=1$ to obtain:
$\begin{align}
& 6-y=1 \\
& y=5
\end{align}$
Hence, the systems of equation are $3x-y=1$ and $x+2y=12$. Solution of the equations is $\left( x,y \right)=\left( 2,5 \right)$.