1. **State the problem:** Solve the system of equations using substitution: $$\begin{cases} 3x - 4y = 11 \\ y = -3x + 1 \end{cases}$$ 2. **Use substitution:** Since the second equation gives $y$ in terms of $x$, substitute $y = -3x + 1$ into the first equation. 3. **Substitute and simplify:** $$3x - 4(-3x + 1) = 11$$ Distribute the $-4$: $$3x + 12x - 4 = 11$$ Combine like terms: $$15x - 4 = 11$$ 4. **Isolate $x$:** Add 4 to both sides: $$15x - \cancel{4} + \cancel{4} = 11 + 4$$ $$15x = 15$$ Divide both sides by 15: $$\frac{15x}{\cancel{15}} = \frac{15}{\cancel{15}}$$ $$x = 1$$ 5. **Find $y$:** Substitute $x=1$ back into $y = -3x + 1$: $$y = -3(1) + 1 = -3 + 1 = -2$$ 6. **Final answer:** The solution to the system is $$(x, y) = (1, -2)$$ This means the two lines intersect at the point $(1, -2)$.