1. **State the problem:** Solve the system of linear equations by graphing: $$\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ to graph easily:** For the first equation: $$x + y = 6 \implies y = 6 - x$$ For the second equation: $$x - y = 2 \implies -y = 2 - x \implies y = x - 2$$ 3. **Graph the lines:** - The first line has slope $-1$ and y-intercept $6$. - The second line has slope $1$ and y-intercept $-2$. 4. **Find the intersection point algebraically to confirm the solution:** Set the right sides equal: $$6 - x = x - 2$$ Add $x$ to both sides: $$6 = 2x - 2$$ Add $2$ to both sides: $$6 + 2 = 2x$$ $$8 = 2x$$ Divide both sides by $2$: $$\frac{8}{\cancel{2}} = \frac{2x}{\cancel{2}} \implies 4 = x$$ Substitute $x=4$ into $y = 6 - x$: $$y = 6 - 4 = 2$$ 5. **Interpretation:** - The lines intersect at the point $(4, 2)$. - This means the system has exactly one solution. - The system is consistent and independent. 6. **Summary:** - Solution: $\boxed{(4, 2)}$ - Number of solutions: 1 - Type of system: Consistent and independent