1. **State the problem:** We have three equations: $$y = -2$$ $$y = x + 3$$ $$y = -2x - 12$$ We need to find their shared solution (the point where all three lines intersect). 2. **Find intersection of the first two lines:** Since $$y = -2$$, substitute into $$y = x + 3$$: $$-2 = x + 3$$ Solve for $$x$$: $$x = -2 - 3 = -5$$ So the intersection is at $$(-5, -2)$$. 3. **Check if this satisfies the third equation $$y = -2x - 12$$:** Substitute $$x = -5$$: $$y = -2(-5) - 12 = 10 - 12 = -2$$ This matches the $$y$$ value. 4. **Therefore, the shared solution of the first three equations is:** $$\boxed{(-5, -2)}$$ 5. **Part b: Find $$c$$ in $$y = 3x + c$$ that shares this solution:** Substitute $$x = -5$$ and $$y = -2$$ into the equation: $$-2 = 3(-5) + c$$ $$-2 = -15 + c$$ Solve for $$c$$: $$c = -2 + 15 = 13$$ 6. **Answer:** $$c = 13$$ **Final answers:** - a) Shared solution: $$(-5, -2)$$ - b) Value of $$c$$: $$13$$