1. **Problem Statement:** Solve the system of linear equations by graphing: $$\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}$$ 2. **Formula and Rules:** To solve by graphing, rewrite each equation in slope-intercept form $y = mx + b$. 3. **Rewrite equations:** - From $x + y = 6$, subtract $x$ from both sides: $$y = 6 - x$$ - From $x - y = 2$, subtract $x$ from both sides: $$-y = 2 - x$$ Multiply both sides by $-1$: $$y = x - 2$$ 4. **Graph the lines:** - Line 1: $y = 6 - x$ - Line 2: $y = x - 2$ 5. **Find intersection point:** Set $6 - x = x - 2$: $$6 - x = x - 2$$ Add $x$ to both sides: $$6 = 2x - 2$$ Add $2$ to both sides: $$8 = 2x$$ Divide both sides by $2$: $$\cancel{2x}^\cancel{2} = \frac{8}{\cancel{2}}$$ $$x = 4$$ 6. **Find $y$ value:** Substitute $x=4$ into $y = 6 - x$: $$y = 6 - 4 = 2$$ 7. **Solution:** The lines intersect at $(4, 2)$. 8. **Type of system:** Since the lines intersect at exactly one point, the system is consistent and independent. 9. **Number of solutions:** There is exactly one solution. 10. **Name of solution:** The solution is the point $(4, 2)$ where the two lines intersect.