1. **State the problem:** We have a track made of 9 segments, each either 6m or 10m long, and the total length is 74m. 2. **Define variables:** Let $x$ be the number of 6m segments and $y$ be the number of 10m segments. 3. **Write equations:** - Total segments: $$x + y = 9$$ - Total length: $$6x + 10y = 74$$ 4. **Solve the system:** From the first equation, express $y$ as $$y = 9 - x$$ 5. Substitute into the length equation: $$6x + 10(9 - x) = 74$$ 6. Simplify: $$6x + 90 - 10x = 74$$ 7. Combine like terms: $$\cancel{6x} - \cancel{10x} + 90 = 74$$ $$-4x + 90 = 74$$ 8. Subtract 90 from both sides: $$-4x = 74 - 90$$ $$-4x = -16$$ 9. Divide both sides by $-4$: $$x = \frac{-16}{-4} = 4$$ 10. Find $y$: $$y = 9 - 4 = 5$$ **Answer:** There are 4 short 6m segments and 5 long 10m segments.