1. **State the problem:** Solve the system of equations using elimination: $$-5x + 9y = -37$$ $$-x + 2y = -9$$ 2. **Write down the equations:** Equation 1: $$-5x + 9y = -37$$ Equation 2: $$-x + 2y = -9$$ 3. **Goal:** Eliminate one variable by making the coefficients of either $$x$$ or $$y$$ the same (or opposites). 4. **Multiply Equation 2 by 5** to align the $$x$$ coefficients with Equation 1: $$5 \times (-x + 2y) = 5 \times (-9)$$ which gives $$-5x + 10y = -45$$ 5. **Subtract Equation 1 from this new equation:** $$(-5x + 10y) - (-5x + 9y) = -45 - (-37)$$ Simplify: $$-5x + 10y + 5x - 9y = -45 + 37$$ $$ (\cancel{-5x} + \cancel{5x}) + (10y - 9y) = -8$$ $$ y = -8$$ 6. **Substitute $$y = -8$$ into Equation 2:** $$-x + 2(-8) = -9$$ $$-x - 16 = -9$$ 7. **Solve for $$x$$:** $$-x = -9 + 16$$ $$-x = 7$$ $$x = -7$$ 8. **Final answer:** $$\boxed{(-7, -8)}$$ This is the solution to the system of equations.