Let's solve the system of equations given:
- \( 3x + 2y = 2 \)
- \( -2x + y = 8 \)
To solve this system, we can use substitution or elimination. Here, I'll use the elimination method.
From the second equation, we can express \( y \) in terms of \( x \):
\[ y = 2x + 8 \]
Now, substitute \( y \) in the first equation:
\[ 3x + 2(2x + 8) = 2 \]
Expanding this gives:
\[ 3x + 4x + 16 = 2 \]
Combining like terms:
\[ 7x + 16 = 2 \]
Now, isolate \( x \):
\[ 7x = 2 - 16 \] \[ 7x = -14 \] \[ x = -2 \]
Now substitute \( x = -2 \) back into the expression for \( y \):
\[ y = 2(-2) + 8 \] \[ y = -4 + 8 \] \[ y = 4 \]
So, the solution to the system of equations is:
\[ (x, y) = (-2, 4) \]
Now, checking the response options, the correct answer is:
(-2, 4).