To solve the system of equations:
- \( 3x + 2y = 2 \)
- \( -2x + y = 8 \)
We can either solve it graphically or algebraically. Here, I'll solve it algebraically.
From the second equation, we can express \( y \) in terms of \( x \):
\[ y = 2x + 8 \]
Now, we can substitute this expression for \( y \) into 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 that we have \( x \), substitute back to find \( y \):
\[ y = 2(-2) + 8 \] \[ y = -4 + 8 \] \[ y = 4 \]
The solution to the system of equations is:
\[ (x, y) = (-2, 4) \]
Therefore, the answer is \((-2, 4)\).