1. **Problem:** Solve the system of equations: $$3x + 5y = 24$$ $$3x + 21 = 5y$$ 2. **Rewrite the second equation:** $$3x + 21 = 5y \implies 3x - 5y = -21$$ 3. **System now:** $$3x + 5y = 24$$ $$3x - 5y = -21$$ 4. **Add the two equations to eliminate $y$: ** $$ (3x + 5y) + (3x - 5y) = 24 + (-21) $$ $$ 6x = 3 $$ $$ x = \frac{3}{6} = \frac{1}{2} $$ 5. **Substitute $x=\frac{1}{2}$ into the first equation:** $$3\left(\frac{1}{2}\right) + 5y = 24$$ $$\frac{3}{2} + 5y = 24$$ $$5y = 24 - \frac{3}{2} = \frac{48}{2} - \frac{3}{2} = \frac{45}{2}$$ $$y = \frac{45}{2} \times \frac{1}{5} = \frac{45}{10} = \frac{9}{2} = 4.5$$ 6. **Solution:** $$\boxed{\left(\frac{1}{2}, \frac{9}{2}\right)}$$ **Note:** The provided answer (-2, 3) does not satisfy the system as given, so this is the correct solution. --- **Summary:** - Used elimination method to solve the first system. - Found $x=\frac{1}{2}$ and $y=\frac{9}{2}$. This completes the solution for the first system.