1. **State the problem:** We need to find the values of $\alpha$ and $b$ given the system of equations: $$12 = 8 + \alpha$$ $$\alpha + 9 = 10 + b$$ 2. **Solve for $\alpha$ from the first equation:** Subtract 8 from both sides: $$12 - 8 = \alpha$$ $$4 = \alpha$$ So, $\alpha = 4$. 3. **Substitute $\alpha = 4$ into the second equation:** $$4 + 9 = 10 + b$$ Simplify the left side: $$13 = 10 + b$$ 4. **Solve for $b$:** Subtract 10 from both sides: $$13 - 10 = b$$ $$3 = b$$ So, $b = 3$. **Final answer:** $$\alpha = 4, \quad b = 3$$