To solve the system of equations 2x + y = 4 and x + y = 2, we can use the method of substitution.

First, solve the second equation for y: y = 2 - x

Next, substitute this expression for y into the first equation:

2x + (2 - x) = 4
2x + 2 - x = 4
x + 2 = 4
x = 2

Now that we have found the value of x, we can substitute it back into the second equation to find the value of y:

2 + y = 2
y = 0

Therefore, the solution to the system of equations is x = 2 and y = 0.