1. **State the problem:** Solve 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 $Y$: $$ (X + Y) + (X - Y) = 2 + 4 $$ $$ 2X + \cancel{Y} - \cancel{Y} = 6 $$ $$ 2X = 6 $$ Divide both sides by 2: $$ \cancel{2}X / \cancel{2} = 6 / 2 $$ $$ X = 3 $$ 3. **Find $Y$ by substituting $X=3$ into one of the original equations:** Using $X + Y = 2$: $$ 3 + Y = 2 $$ Subtract 3 from both sides: $$ Y = 2 - 3 $$ $$ Y = -1 $$ 4. **Solution set:** $$ (X, Y) = (3, -1) $$ 5. **Identify the type of system:** Since there is a unique solution, the system is **consistent and independent**. 6. **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 two lines intersect at the point $(3, -1)$, confirming the solution.