1. **State the problem:** We are given the equation $y = 2x + 9$ and the inequality $4x + 3y \leq 57$. We need to find: a) The maximum value of $x$. b) The maximum value of $y$. 2. **Use the inequality and substitute $y$:** Substitute $y = 2x + 9$ into the inequality: $$4x + 3(2x + 9) \leq 57$$ 3. **Simplify the inequality:** $$4x + 6x + 27 \leq 57$$ $$10x + 27 \leq 57$$ 4. **Solve for $x$:** $$10x \leq 57 - 27$$ $$10x \leq 30$$ $$x \leq 3$$ So, the maximum value of $x$ is $3$. 5. **Find the maximum value of $y$ using $x=3$:** Substitute $x=3$ into $y = 2x + 9$: $$y = 2(3) + 9 = 6 + 9 = 15$$ So, the maximum value of $y$ is $15$. **Final answers:** - Maximum $x = 3$ - Maximum $y = 15$