1. **State the problem:** We need to find the number of solutions to the system of linear equations: $$6x + 5y = 7$$ $$-4x + 11y = 9$$ 2. **Recall the rule:** A system of two linear equations in two variables can have: - Exactly one solution if the lines intersect (i.e., the lines are not parallel). - No solution if the lines are parallel but not coincident. - Infinitely many solutions if the lines are coincident (the same line). 3. **Check if the lines are parallel:** Calculate the ratios of the coefficients of $x$ and $y$: $$\frac{6}{-4} = -\frac{3}{2}$$ $$\frac{5}{11}$$ Since $-\frac{3}{2} \neq \frac{5}{11}$, the slopes are different, so the lines are not parallel. 4. **Conclusion:** Since the lines are not parallel, they intersect at exactly one point. **Final answer:** The system has one solution.