Solve the system of equations:

$x + 2y = 8 \quad \text{(1)}$ $-2x + y = 14 \quad \text{(2)}$

From equation (2), solve for $y$:

$y = 14 + 2x$

Substitute into equation (1):

$x + 2(14 + 2x) = 8$

$x + 28 + 4x = 8$

$5x = -20$

$x = -4$

Substitute back to find $y$:

$y = 14 + 2(-4) = 14 - 8 = 6$

The solution is $(-4, 6)$.