1. **State the problem:** Find values of A and B given the system: $$3A - 2 = 2B$$ $$5A = 3B + 5$$ 2. **Write the equations:** Equation 1: $$3A - 2 = 2B$$ Equation 2: $$5A = 3B + 5$$ 3. **Isolate variables:** From Equation 1, solve for $$B$$: $$3A - 2 = 2B \implies B = \frac{3A - 2}{2}$$ 4. **Substitute into Equation 2:** $$5A = 3\left(\frac{3A - 2}{2}\right) + 5$$ 5. **Simplify the substitution:** $$5A = \frac{9A - 6}{2} + 5$$ Multiply both sides by 2 to clear denominator: $$2 \times 5A = 9A - 6 + 10$$ $$10A = 9A + 4$$ 6. **Isolate A:** $$10A - 9A = 4$$ $$A = 4$$ 7. **Find B using A:** $$B = \frac{3(4) - 2}{2} = \frac{12 - 2}{2} = \frac{10}{2} = 5$$ **Final answers:** $$A = 4$$ $$B = 5$$