1. **State the problem:** We need to find how many solutions the system of equations has: $$y = 9x - 9$$ $$y = -\frac{7}{4}x + \frac{9}{10}$$ 2. **Recall the rule for solutions of linear systems:** - If the lines have different slopes, they intersect at exactly one point (one solution). - If the lines have the same slope but different intercepts, they are parallel and have no solution. - If the lines have the same slope and intercept, they coincide and have infinitely many solutions. 3. **Identify slopes and intercepts:** - First line slope: $9$ - Second line slope: $-\frac{7}{4}$ 4. **Compare slopes:** Since $9 \neq -\frac{7}{4}$, the lines have different slopes. 5. **Conclusion:** The system has exactly one solution because the lines intersect at one point. **Final answer:** One solution.