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Given the inequality:$\newline$$x + 2y \geq 2$$\newline$Erica's goal is to score at least $24$ points in her next playground basketball game. The given inequality represents this goal, where $x$ is the number of $3$-point field goals she scores and $y$ is the number of $2$-point field goals she scores. If she scores $5$ $3$-point field goals, what is the minimum number of $2$-point field goals she must score to meet her scoring goal?