1. **State the problem:** Solve the system of equations by graphing: $$2x + y = 2$$ $$3x + 6y = -6$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ to graph easily:** For the first equation: $$2x + y = 2 \implies y = 2 - 2x$$ For the second equation: $$3x + 6y = -6 \implies 6y = -6 - 3x \implies y = \frac{-6 - 3x}{6} = -1 - \frac{1}{2}x$$ 3. **Graph the lines:** - First line: $y = 2 - 2x$ - Second line: $y = -1 - \frac{1}{2}x$ 4. **Find the intersection point algebraically to confirm the solution:** Set the two expressions for $y$ equal: $$2 - 2x = -1 - \frac{1}{2}x$$ 5. **Solve for $x$:** $$2 - 2x = -1 - \frac{1}{2}x$$ Add $2x$ to both sides: $$2 = -1 + \frac{3}{2}x$$ Add $1$ to both sides: $$3 = \frac{3}{2}x$$ Multiply both sides by $\cancel{\frac{2}{3}}$ to isolate $x$: $$x = 3 \times \cancel{\frac{2}{3}} = 2$$ 6. **Find $y$ by substituting $x=2$ into one of the equations:** Using $y = 2 - 2x$: $$y = 2 - 2(2) = 2 - 4 = -2$$ 7. **Solution:** The lines intersect at the point $$\boxed{(2, -2)}$$ which is the solution to the system. This means the system has one unique solution where the two lines cross.