1. **State the problem:** We have two linear equations: $$7.50x + 15y = 750$$ $$6x + 4y = 700$$ where $x$ and $y$ represent hours worked and tasks done for Seth and Karen respectively. 2. **Goal:** Solve for $x$ and $y$ to find the number of hours and tasks. 3. **Rewrite the first equation for clarity:** $$7.5x + 15y = 750$$ 4. **Use substitution or elimination. Let's use elimination.** 5. **Multiply the first equation by 4 and the second by 15 to align $y$ coefficients:** $$4(7.5x + 15y) = 4(750) \Rightarrow 30x + 60y = 3000$$ $$15(6x + 4y) = 15(700) \Rightarrow 90x + 60y = 10500$$ 6. **Subtract the first new equation from the second:** $$\cancel{90x} + 60y - (\cancel{30x} + 60y) = 10500 - 3000$$ $$90x - 30x + 60y - 60y = 7500$$ $$60x = 7500$$ 7. **Solve for $x$:** $$x = \frac{7500}{60} = 125$$ 8. **Substitute $x=125$ into the first original equation:** $$7.5(125) + 15y = 750$$ $$937.5 + 15y = 750$$ 9. **Isolate $y$:** $$15y = 750 - 937.5 = -187.5$$ $$y = \frac{-187.5}{15} = -12.5$$ 10. **Interpretation:** Seth works 125 hours and mows -12.5 lawns, which is not possible physically, indicating a problem with the model or data. **Final answer:** $$x = 125, \quad y = -12.5$$