1. **State the problem:** We are asked to find how many solutions the system of linear equations has: $$y = -\frac{3}{4}x - 6$$ $$y = -\frac{3}{4}x - 6$$ 2. **Understand the system:** Both equations are exactly the same. This means the two lines coincide perfectly. 3. **Recall the rule:** When two lines are identical, they have infinitely many points in common. 4. **Conclusion:** Therefore, the system has an infinite number of solutions. **Final answer:** an infinite number of solutions