1. **State the problem:** Find the intersection point of the two lines given by the equations: $$y = -3x + 15$$ and $$-x - y = -9$$ 2. **Rewrite the second equation:** Solve for $y$ in terms of $x$. $$-x - y = -9$$ Add $x$ to both sides: $$-y = -9 + x$$ Multiply both sides by $-1$: $$\cancel{-1} \times (-y) = \cancel{-1} \times (-9 + x)$$ $$y = 9 - x$$ 3. **Set the two expressions for $y$ equal to find $x$:** $$-3x + 15 = 9 - x$$ 4. **Solve for $x$:** Add $3x$ to both sides: $$-3x + 3x + 15 = 9 - x + 3x$$ $$15 = 9 + 2x$$ Subtract 9 from both sides: $$15 - 9 = 9 - 9 + 2x$$ $$6 = 2x$$ Divide both sides by 2: $$\frac{6}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$3 = x$$ 5. **Find $y$ by substituting $x=3$ into one of the original equations:** Using $y = 9 - x$: $$y = 9 - 3 = 6$$ 6. **Final answer:** The lines intersect at the point $$(x, y) = (3, 6)$$