1. The problem is to graph the system of equations: $$y = x + 1$$ $$y = -x + 1$$ 2. These are two linear equations representing straight lines. The solution to the system is the point(s) where the lines intersect. 3. To find the intersection, set the right-hand sides equal: $$x + 1 = -x + 1$$ 4. Solve for $x$: $$x + 1 = -x + 1$$ $$x + x = 1 - 1$$ $$2x = 0$$ $$x = \cancel{\frac{0}{2}}0$$ 5. Substitute $x=0$ into one of the equations to find $y$: $$y = 0 + 1 = 1$$ 6. The lines intersect at the point $(0,1)$. 7. To graph: - The line $y = x + 1$ has slope 1 and y-intercept 1. - The line $y = -x + 1$ has slope -1 and y-intercept 1. 8. Both lines cross the y-axis at $(0,1)$ and slope up and down respectively. 9. The graph shows two lines intersecting at $(0,1)$, confirming the solution.