## Integer Programming, Valid Inequalities

Prove that $y_2+y_3+2y_4 \leq 6$ is valid for

$X= \{ y \in \mathbb{Z}_{+}^{4}: 4y_1+5y_2+9y_3+12y_4 \leq 34 \}$

I don't completely understand this because it seems that y_3 could be 6, which would be greater than 34.