To solve the system of equations:
- \(3x + 2y = 2\)
- \(-2x + y = 8\)
we can start by solving for \(y\) in the second equation:
From \(-2x + y = 8\), we can express \(y\) as: \[ y = 2x + 8 \]
Now, we substitute \(y\) in the first equation:
\[ 3x + 2(2x + 8) = 2 \]
Expanding this, we get: \[ 3x + 4x + 16 = 2 \]
Combining like terms: \[ 7x + 16 = 2 \]
Next, we isolate \(x\): \[ 7x = 2 - 16 \] \[ 7x = -14 \] \[ x = -2 \]
Now we substitute \(x = -2\) back into the equation for \(y\): \[ y = 2(-2) + 8 \] \[ y = -4 + 8 \] \[ y = 4 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-2, 4) \]
Among the provided responses, the correct answer is: (-2, 4).