1. **State the problem:** Find the intersection point of the two lines given by the equations derived from the inequalities: $$3x - 5y = 2$$ $$8x + 15y = 9$$ 2. **Method:** To find the intersection, solve the system of linear equations simultaneously. 3. **Step 1: Multiply the first equation by 3 to align coefficients of $y$:** $$3(3x - 5y) = 3(2) \Rightarrow 9x - 15y = 6$$ 4. **Step 2: Write the second equation:** $$8x + 15y = 9$$ 5. **Step 3: Add the two equations to eliminate $y$:** $$9x - 15y + 8x + 15y = 6 + 9$$ $$17x = 15$$ 6. **Step 4: Solve for $x$:** $$x = \frac{15}{17}$$ 7. **Step 5: Substitute $x$ back into the first equation to solve for $y$:** $$3\left(\frac{15}{17}\right) - 5y = 2$$ $$\frac{45}{17} - 5y = 2$$ 8. **Step 6: Isolate $y$:** $$-5y = 2 - \frac{45}{17} = \frac{34}{17} - \frac{45}{17} = -\frac{11}{17}$$ $$y = \frac{-\frac{11}{17}}{-5} = \frac{11}{85}$$ 9. **Final answer:** The intersection point is $$\boxed{\left(\frac{15}{17}, \frac{11}{85}\right)}$$