1. **State the problem:** Solve the system of equations: $$A + B = 2$$ $$2A + B = 1$$ 2. **Use substitution or elimination method:** Here, we use elimination. 3. **Subtract the first equation from the second:** $$\cancel{2A + B} - \cancel{(A + B)} = 1 - 2$$ $$2A + B - A - B = -1$$ $$A = -1$$ 4. **Substitute $A = -1$ into the first equation:** $$-1 + B = 2$$ 5. **Solve for $B$:** $$B = 2 + 1 = 3$$ 6. **Final answer:** $$A = -1, \quad B = 3$$