1. **State the problem:** Solve the first system of linear equations for variables $f$ and $g$: $$3(3f + 2g) = 5 - f$$ $$4g + 5 = 2(g - 5f)$$ 2. **Rewrite each equation:** Expand the first equation: $$3 \times 3f + 3 \times 2g = 5 - f$$ $$9f + 6g = 5 - f$$ Bring all terms to one side: $$9f + 6g + f = 5$$ $$10f + 6g = 5$$ The second equation: $$4g + 5 = 2g - 10f$$ Bring all terms to one side: $$4g - 2g + 5 + 10f = 0$$ $$2g + 10f + 5 = 0$$ 3. **Simplify the system:** $$10f + 6g = 5$$ $$10f + 2g = -5$$ 4. **Subtract the second equation from the first to eliminate $f$:** $$\cancel{10f} + 6g - (\cancel{10f} + 2g) = 5 - (-5)$$ $$6g - 2g = 5 + 5$$ $$4g = 10$$ 5. **Solve for $g$:** $$g = \frac{10}{4} = \frac{5}{2}$$ 6. **Substitute $g = \frac{5}{2}$ into one of the original simplified equations to find $f$:** Using $$10f + 2g = -5$$: $$10f + 2 \times \frac{5}{2} = -5$$ $$10f + 5 = -5$$ 7. **Solve for $f$:** $$10f = -5 - 5$$ $$10f = -10$$ $$f = \frac{-10}{10} = -1$$ **Final answer:** $$f = -1, \quad g = \frac{5}{2}$$