1. **State the problem:** Solve the system of equations using elimination: $$-4x - 9y = 26$$ $$8x + 9y = -34$$ 2. **Add to eliminate y:** Adding the two equations cancels out $y$ because $-9y + 9y = 0$: $$(-4x - 9y) + (8x + 9y) = 26 + (-34)$$ $$-4x + 8x + \cancel{-9y} + \cancel{9y} = -8$$ $$4x = -8$$ 3. **Solve for $x$:** $$x = \frac{-8}{4} = -2$$ 4. **Substitute $x = -2$ into one original equation to find $y$:** Using the first equation: $$-4(-2) - 9y = 26$$ $$8 - 9y = 26$$ 5. **Isolate $y$:** $$-9y = 26 - 8$$ $$-9y = 18$$ 6. **Solve for $y$:** $$y = \frac{18}{-9} = -2$$ 7. **Check by subtracting to eliminate $y$:** Subtract second equation from first: $$(-4x - 9y) - (8x + 9y) = 26 - (-34)$$ $$-4x - 9y - 8x - 9y = 26 + 34$$ $$-12x - 18y = 60$$ This does not eliminate $y$, so subtraction is not useful here. 8. **Add to eliminate $x$:** Add equations: $$(-4x - 9y) + (8x + 9y) = 26 + (-34)$$ $$4x + 0 = -8$$ Already done in step 2. 9. **Subtract to eliminate $x$:** Subtract second from first: $$(-4x - 9y) - (8x + 9y) = 26 - (-34)$$ $$-12x - 18y = 60$$ Does not eliminate $x$ alone. **Final solution:** $$x = -2, \quad y = -2$$