HMMT November 2020 U14

A point $(x, y)$ is selected uniformly at random from the unit square $S=\{(x, y) \mid 0 \leq x \leq 1,0 \leq$ $y \leq 1\}$. If the probability that $(3 x+2 y, x+4 y)$ is in $S$ is $\frac{a}{b}$, where $a, b$ are relatively prime positive integers, compute $100 a+b$.