1. **State the problem:** Find the intersection point of the lines given by the equations $$4x - 18 = -3y$$ and $$5x - 2y = 11$$. 2. **Rewrite the equations in standard form:** From the first equation: $$4x - 18 = -3y \implies 4x + 3y = 18$$ The second equation is already: $$5x - 2y = 11$$ 3. **Use the system of linear equations:** $$\begin{cases} 4x + 3y = 18 \\ 5x - 2y = 11 \end{cases}$$ 4. **Solve for one variable:** Multiply the first equation by 2 and the second by 3 to eliminate $y$: $$2(4x + 3y) = 2(18) \implies 8x + 6y = 36$$ $$3(5x - 2y) = 3(11) \implies 15x - 6y = 33$$ 5. **Add the two equations:** $$8x + 6y + 15x - 6y = 36 + 33 \implies 23x = 69$$ 6. **Solve for $x$:** $$x = \frac{69}{23} = 3$$ 7. **Substitute $x=3$ into one of the original equations to find $y$:** Using $4x + 3y = 18$: $$4(3) + 3y = 18 \implies 12 + 3y = 18 \implies 3y = 6 \implies y = 2$$ 8. **Final answer:** The lines intersect at the point $$\boxed{(3, 2)}$$.