1. **State the problem:** Solve the simultaneous equations: $$\frac{x}{2} + \frac{y}{3} = 5$$ $$x - y = 1$$ 2. **Rewrite the first equation:** Multiply both sides by 6 (the least common multiple of 2 and 3) to clear denominators: $$6 \times \left(\frac{x}{2} + \frac{y}{3}\right) = 6 \times 5$$ $$3x + 2y = 30$$ 3. **Use the second equation:** From $$x - y = 1$$, express $$x$$ in terms of $$y$$: $$x = y + 1$$ 4. **Substitute into the first equation:** Replace $$x$$ with $$y + 1$$ in $$3x + 2y = 30$$: $$3(y + 1) + 2y = 30$$ 5. **Simplify and solve for $$y$$:** $$3y + 3 + 2y = 30$$ $$5y + 3 = 30$$ $$5y = 27$$ $$y = \frac{27}{5} = 5.4$$ 6. **Find $$x$$:** Substitute $$y = 5.4$$ back into $$x = y + 1$$: $$x = 5.4 + 1 = 6.4$$ **Final answer:** $$x = 6.4$$, $$y = 5.4$$