1. **State the problem:** Solve the system of equations: $$5y = 2x - 6$$ $$3x - 2y = -10$$ 2. **Rewrite the first equation to express $y$ in terms of $x$: ** $$5y = 2x - 6$$ $$y = \frac{2x - 6}{5}$$ 3. **Substitute $y$ into the second equation:** $$3x - 2\left(\frac{2x - 6}{5}\right) = -10$$ 4. **Multiply both sides by 5 to clear the denominator:** $$5 \times 3x - 5 \times 2 \times \frac{2x - 6}{5} = 5 \times (-10)$$ $$15x - 2(2x - 6) = -50$$ 5. **Distribute and simplify:** $$15x - (4x - 12) = -50$$ $$15x - 4x + 12 = -50$$ $$11x + 12 = -50$$ 6. **Isolate $x$:** $$11x = -50 - 12$$ $$11x = -62$$ $$x = \frac{-62}{11}$$ 7. **Substitute $x$ back into the expression for $y$:** $$y = \frac{2\left(\frac{-62}{11}\right) - 6}{5}$$ $$y = \frac{\frac{-124}{11} - 6}{5}$$ 8. **Convert 6 to fraction with denominator 11:** $$6 = \frac{66}{11}$$ 9. **Simplify numerator:** $$\frac{-124}{11} - \frac{66}{11} = \frac{-190}{11}$$ 10. **Divide by 5:** $$y = \frac{\frac{-190}{11}}{5} = \frac{-190}{11} \times \frac{1}{5} = \frac{-190}{55}$$ 11. **Simplify fraction:** $$\frac{-190}{55} = \frac{\cancel{-190}^{\times 5 \times 38}}{\cancel{55}^{\times 5 \times 11}} = \frac{-38}{11}$$ **Final solution:** $$x = \frac{-62}{11}, \quad y = \frac{-38}{11}$$