1. **State the problem:** Solve and graph the system of linear equations: $$\begin{cases} X + Y = 2 \\ X - Y = 4 \end{cases}$$ 2. **Use substitution or elimination to solve:** Add the two equations to eliminate $Y$: $$ (X + Y) + (X - Y) = 2 + 4 $$ $$ 2X + \cancel{Y} - \cancel{Y} = 6 $$ $$ 2X = 6 $$ $$ X = \frac{6}{2} = 3 $$ 3. **Find $Y$ by substituting $X=3$ into one of the original equations:** Using $X + Y = 2$: $$ 3 + Y = 2 $$ $$ Y = 2 - 3 = -1 $$ 4. **Solution set:** $$ \boxed{(X, Y) = (3, -1)} $$ 5. **Check the solution:** Substitute into $X - Y = 4$: $$ 3 - (-1) = 3 + 1 = 4 $$ Correct. 6. **Identify the type of system:** Since there is exactly one unique solution, the system is **consistent and independent**. 7. **Graphing:** - The line $X + Y = 2$ can be rewritten as $Y = 2 - X$. - The line $X - Y = 4$ can be rewritten as $Y = X - 4$. - The lines intersect at $(3, -1)$. 8. **Given $X=0$ and $Y=0$:** - For $X=0$, from $X + Y = 2$, $Y=2$. - For $Y=0$, from $X + Y = 2$, $X=2$. These points help plot the lines.