1. **Stating the problem:** We are given the system of equations: $$\frac{9}{2}x + 4y = 27$$ $$\frac{3}{2}x + 4y = 21$$ We need to find the value of $$\frac{17}{2}x + 6y$$ at the solution point $$(x,y)$$. 2. **Formula and approach:** To solve for $x$ and $y$, we use the method of elimination or substitution. Since both equations have $4y$, subtracting one from the other will eliminate $y$. 3. **Subtract the second equation from the first:** $$\left(\frac{9}{2}x + 4y\right) - \left(\frac{3}{2}x + 4y\right) = 27 - 21$$ Simplify: $$\frac{9}{2}x - \frac{3}{2}x = 6$$ $$\frac{6}{2}x = 6$$ $$3x = 6$$ $$x = 2$$ 4. **Substitute $x=2$ into the second equation to find $y$:** $$\frac{3}{2} \times 2 + 4y = 21$$ $$3 + 4y = 21$$ $$4y = 18$$ $$y = \frac{18}{4} = \frac{9}{2} = 4.5$$ 5. **Calculate the required expression:** $$\frac{17}{2}x + 6y = \frac{17}{2} \times 2 + 6 \times \frac{9}{2}$$ $$= 17 + 6 \times 4.5$$ $$= 17 + 27 = 44$$ 6. **Answer:** The value of $$\frac{17}{2}x + 6y$$ is **44**, which corresponds to option C.