38. Solve the following system of equations over $\mathbb{Z}_5$
$x + y + 2z + w = 1$
$2x + 2y + z + 2w = 2$
$2x + y + z + w = 1$
$\circ \quad x = 1 + 2s + t, \quad y = 2 + 2s + t, \quad z = s, \quad w = t \qquad (s, t \in \mathbb{Z}_5)$
$\circ \quad x = 1 + 3s + 4t, \quad y = 2 + 4s + 3t, \quad z = s, \quad w = t \qquad (s, t \in \mathbb{Z}_5)$
$\circ \quad x = 1 + 2s + 3t, \quad y = 2 + 3s + 4t, \quad z = s, \quad w = t \qquad (s, t \in \mathbb{Z}_5)$
$\circ \quad x = 2 + 4s + 3t, \quad y = 1 + 3s + 4t, \quad z = s, \quad w = t \qquad (s, t \in \mathbb{Z}_5)$
$\circ \quad x = 4 + 3s + 4t, \quad y = 4 + 4s + 3t, \quad z = s, \quad w = t \qquad (s, t \in \mathbb{Z}_5)$