1. We are asked to solve the system of equations by elimination: $$\begin{cases} y = -3x + 5 \\ y = -8x + 25 \end{cases}$$ 2. Since both equations equal $y$, we can set them equal to each other: $$-3x + 5 = -8x + 25$$ 3. Add $8x$ to both sides to eliminate $x$ on the right: $$-3x + 8x + 5 = -8x + 8x + 25$$ $$5x + 5 = 25$$ 4. Subtract 5 from both sides: $$5x + \cancel{5} - \cancel{5} = 25 - 5$$ $$5x = 20$$ 5. Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{20}{\cancel{5}}$$ $$x = 4$$ 6. Substitute $x=4$ back into one of the original equations to find $y$. Using $y = -3x + 5$: $$y = -3(4) + 5 = -12 + 5 = -7$$ 7. The solution to the system is: $$(x,y) = (4, -7)$$ This means the two lines intersect at the point $(4, -7)$.