1. **State the problem:** We need to solve the system of linear equations graphically: $$y = x + 1$$ $$4x - 2y = -6$$ 2. **Rewrite the second equation in slope-intercept form:** Start with: $$4x - 2y = -6$$ Subtract $4x$ from both sides: $$-2y = -4x - 6$$ Divide both sides by $-2$: $$y = \frac{\cancel{-2}y}{\cancel{-2}} = \frac{-4x - 6}{-2} = \frac{-4x}{-2} + \frac{-6}{-2} = 2x + 3$$ 3. **Graph the two lines:** - The first line is $y = x + 1$, which has slope $1$ and y-intercept $1$. - The second line is $y = 2x + 3$, which has slope $2$ and y-intercept $3$. 4. **Find the point of intersection (POI) algebraically:** Set the two expressions for $y$ equal: $$x + 1 = 2x + 3$$ Subtract $x$ from both sides: $$1 = x + 3$$ Subtract $3$ from both sides: $$1 - 3 = x$$ $$x = -2$$ 5. **Find $y$ by substituting $x = -2$ into one of the equations:** Using $y = x + 1$: $$y = -2 + 1 = -1$$ 6. **Final answer:** The point of intersection is at $$\boxed{(-2, -1)}$$ This is the solution to the system of equations.