To solve the system of linear equations:

1. \( 2x - y = 3 \)
2. \( x - y = 2 \)

we can use either the substitution method or the elimination method. Here, I'll use the elimination method.

First, let's subtract the second equation from the first equation to eliminate \( y \):

\[ (2x - y) - (x - y) = 3 - 2 \]

Simplify the left side:

\[ 2x - y - x + y = 1 \]

Combine like terms:

\[ x = 1 \]

Now that we have \( x = 1 \), we can substitute this value back into the second equation to find \( y \):

\[ x - y = 2 \]

Substitute \( x = 1 \):

\[ 1 - y = 2 \]

Solve for \( y \):

\[ -y = 2 - 1 \]
\[ -y = 1 \]
\[ y = -1 \]

So, the solution to the system of equations is:

\[ x = 1 \]
\[ y = -1 \]

To verify, we can substitute \( x = 1 \) and \( y = -1 \) back into the original equations:

1. \( 2(1) - (-1) = 3 \)
\[ 2 + 1 = 3 \]
\[ 3 = 3 \] (True)

2. \( 1 - (-1) = 2 \)
\[ 1 + 1 = 2 \]
\[ 2 = 2 \] (True)

Both equations are satisfied, so the solution \( x = 1 \) and \( y = -1 \) is correct.