To solve the system of equations:
[tex]\[
\begin{array}{l}
3x - 2y = 4 \\
x + y = 2
\end{array}
\][/tex]
we will use the substitution or elimination method. Here, I'll demonstrate using the substitution method.
1. Solve the second equation for [tex]\( x \)[/tex]:
[tex]\[
x + y = 2 \implies x = 2 - y
\][/tex]
2. Substitute [tex]\( x = 2 - y \)[/tex] into the first equation:
[tex]\[
3(2 - y) - 2y = 4
\][/tex]
3. Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[
6 - 3y - 2y = 4 \\
6 - 5y = 4 \\
-5y = 4 - 6 \\
-5y = -2 \\
y = \frac{2}{5}
\][/tex]
4. Substitute [tex]\( y = \frac{2}{5} \)[/tex] back into the equation [tex]\( x = 2 - y \)[/tex]:
[tex]\[
x = 2 - \frac{2}{5} \\
x = \frac{10}{5} - \frac{2}{5} \\
x = \frac{8}{5}
\][/tex]
Thus, the values are:
[tex]\[
x = \frac{8}{5}, \quad y = \frac{2}{5}
\][/tex]
So, the correct choice is [tex]\( \boxed{D} \)[/tex].
