1. **State the problem:** Determine how many solutions the system of equations has: $$y = -5x + 8$$ $$y = -\frac{9}{7}x + \frac{7}{10}$$ 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 the slopes:** - First line slope: $m_1 = -5$ - Second line slope: $m_2 = -\frac{9}{7}$ 4. **Compare the slopes:** Since $-5 \neq -\frac{9}{7}$, the lines have different slopes. 5. **Conclusion:** The system has exactly one solution because the lines intersect at one point. **Final answer:** one solution