To solve the system of linear equations:

1. \( 2x + y = 4 \)
2. \( x - y = 2 \)

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

First, let's add the two equations together to eliminate \( y \):

\[
(2x + y) + (x - y) = 4 + 2
\]

This simplifies to:

\[
3x = 6
\]

Solving for \( x \):

\[
x = \frac{6}{3} = 2
\]

Now that we have \( x = 2 \), we can substitute this value back into one of the original equations to solve for \( y \). Let's use the second equation:

\[
x - y = 2
\]

Substitute \( x = 2 \):

\[
2 - y = 2
\]

Solving for \( y \):

\[
-y = 2 - 2
\]

\[
-y = 0
\]

\[
y = 0
\]

So, the solution to the system of equations is:

\[
x = 2, \quad y = 0
\]

To verify, we can substitute \( x = 2 \) and \( y = 0 \) back into the original equations:

1. \( 2(2) + 0 = 4 \) which simplifies to \( 4 = 4 \) (True)
2. \( 2 - 0 = 2 \) which simplifies to \( 2 = 2 \) (True)

Both equations are satisfied, so the solution is correct. The solution to the system is:

\[
(x, y) = (2, 0)
\]