1. **State the problem:** We need to find the number of solutions to the system of equations: $$y = x - 6$$ $$y = \frac{4}{9}x - \frac{9}{10}$$ 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 never intersect (no solution). - If the lines have the same slope and same intercept, they coincide (infinitely many solutions). 3. **Identify slopes and intercepts:** - First line slope: $m_1 = 1$, intercept: $b_1 = -6$ - Second line slope: $m_2 = \frac{4}{9}$, intercept: $b_2 = -\frac{9}{10}$ 4. **Compare slopes:** Since $m_1 = 1$ and $m_2 = \frac{4}{9}$, and $1 \neq \frac{4}{9}$, the lines have different slopes. 5. **Conclusion:** Lines with different slopes intersect at exactly one point. **Final answer:** The system has **one solution**.