1. Stating the problem: We need to graph the system of equations: $$x+2y=6$$ $$x-y=-6$$ 2. Solve each equation for $y$ to express in slope-intercept form $y=mx+b$: From the first equation: $$x+2y=6 \\ 2y=6 - x \\ y=\frac{6 - x}{2} = 3 - \frac{x}{2}$$ From the second equation: $$x - y = -6 \\ -y = -6 - x \\ y = x + 6$$ 3. The two lines to graph are: $$y = 3 - \frac{1}{2}x$$ $$y = x + 6$$ 4. (Optional) Find the intersection point by solving the system: Set the right sides equal: $$3 - \frac{x}{2} = x + 6$$ Multiply both sides by 2 to clear fraction: $$6 - x = 2x + 12$$ Bring variables to one side: $$6 - x - 2x = 12 \\ 6 - 3x = 12$$ Subtract 6: $$-3x = 6$$ Divide by -3: $$x = -2$$ Substitute back to find $y$: $$y = x + 6 = -2 + 6 = 4$$ Hence, the two lines intersect at point $(-2, 4)$. 5. Conclusion: To graph, plot the two lines: - Line 1: slope $-\frac{1}{2}$, y-intercept 3. - Line 2: slope 1, y-intercept 6. They intersect at $(-2, 4)$.