1. **State the problem:** Find the system of linear equations for two lines intersecting at the point $(-2, -1)$. 2. **Identify points and slopes:** - Line 1 passes through $(0, 5)$ and $(-2, -1)$. - Line 2 passes through $(0, -2)$ and $(-2, -1)$. 3. **Calculate slope for Line 1:** $$m_1 = \frac{5 - (-1)}{0 - (-2)} = \frac{6}{2} = 3$$ 4. **Write equation for Line 1 using point-slope form:** $$y - y_1 = m_1(x - x_1)$$ Using point $(0, 5)$: $$y - 5 = 3(x - 0)$$ $$y = 3x + 5$$ 5. **Calculate slope for Line 2:** $$m_2 = \frac{-2 - (-1)}{0 - (-2)} = \frac{-1}{2} = -\frac{1}{2}$$ 6. **Write equation for Line 2 using point-slope form:** Using point $(0, -2)$: $$y - (-2) = -\frac{1}{2}(x - 0)$$ $$y + 2 = -\frac{1}{2}x$$ $$y = -\frac{1}{2}x - 2$$ 7. **Final system of equations:** $$\begin{cases} y = 3x + 5 \\ y = -\frac{1}{2}x - 2 \end{cases}$$ These two lines intersect at $(-2, -1)$ as given.