1. **State the problem:** We are given two linear equations representing monthly earnings: $$7.50x + 15y = 750$$ $$6x + 4y = 700$$ where $x$ and $y$ represent hours worked and number of lawns mowed or dogs walked respectively. 2. **Goal:** Solve the system of equations to find values of $x$ and $y$ that satisfy both equations. 3. **Rewrite equations for clarity:** $$7.5x + 15y = 750$$ $$6x + 4y = 700$$ 4. **Use elimination or substitution. Here, use elimination:** Multiply the second equation by $\frac{15}{4}$ to align coefficients of $y$: $$6x \times \frac{15}{4} + 4y \times \frac{15}{4} = 700 \times \frac{15}{4}$$ which simplifies to: $$\frac{90}{4}x + 15y = 2625$$ or $$22.5x + 15y = 2625$$ 5. **Subtract the first equation from this new equation:** $$\left(22.5x + 15y\right) - \left(7.5x + 15y\right) = 2625 - 750$$ which simplifies to: $$\cancel{15y} + 22.5x - 7.5x - \cancel{15y} = 1875$$ $$15x = 1875$$ 6. **Solve for $x$:** $$x = \frac{1875}{15} = 125$$ 7. **Substitute $x=125$ into the first equation to find $y$:** $$7.5(125) + 15y = 750$$ $$937.5 + 15y = 750$$ $$15y = 750 - 937.5 = -187.5$$ $$y = \frac{-187.5}{15} = -12.5$$ 8. **Interpretation:** $x=125$ hours and $y=-12.5$ lawns/dogs, but negative $y$ may not make sense in context, indicating no valid positive solution for $y$. **Final answer:** $$x = 125, \quad y = -12.5$$