Question 130
Determine the integer values of $x$ and $y$ such that
$$
x - 3y + 4 = 0 \quad \text{and} \quad \sqrt{x^{2} + 7y^{2} + 8x + 8y + 4} \in \mathbb{Q}
$$
$$
x - 3y + 4 = 0 \quad \text{and} \quad \sqrt{x^{2} + 7y^{2} + 8x + 8y + 4} \in \mathbb{Q}
$$