1. **State the problem:** We are given a system of equations: $$x + y = 5$$ $$x^2 + y = 11$$ One point of intersection is $(3, 2)$. We need to find the coordinates of the other point where the line and parabola intersect. 2. **Use substitution:** From the first equation, solve for $y$: $$y = 5 - x$$ 3. **Substitute into the second equation:** Replace $y$ in the second equation with $5 - x$: $$x^2 + (5 - x) = 11$$ 4. **Simplify the equation:** $$x^2 + 5 - x = 11$$ $$x^2 - x + 5 = 11$$ $$x^2 - x + 5 - 11 = 0$$ $$x^2 - x - 6 = 0$$ 5. **Factor the quadratic:** $$x^2 - x - 6 = (x - 3)(x + 2) = 0$$ 6. **Solve for $x$:** $$x - 3 = 0 \Rightarrow x = 3$$ $$x + 2 = 0 \Rightarrow x = -2$$ 7. **Find corresponding $y$ values:** For $x = 3$: $$y = 5 - 3 = 2$$ For $x = -2$: $$y = 5 - (-2) = 5 + 2 = 7$$ 8. **Answer:** The other point of intersection is $(-2, 7)$.