1. **Problem Statement:** Determine whether the system $\begin{cases} 2x - y = 7 \\ 3x - y = 5 \end{cases}$ is dependent, consistent, or independent. 2. **Formula and Rules:** - A system is **consistent** if it has at least one solution. - It is **inconsistent** if it has no solution. - It is **dependent** if the equations represent the same line (infinitely many solutions). - It is **independent** if the equations represent different lines intersecting at exactly one point. 3. **Step 1: Write the system:** $$\begin{cases} 2x - y = 7 \\ 3x - y = 5 \end{cases}$$ 4. **Step 2: Subtract the first equation from the second to eliminate $y$:** $$ (3x - y) - (2x - y) = 5 - 7 $$ $$ 3x - y - 2x + y = -2 $$ $$ x = -2 $$ 5. **Step 3: Substitute $x = -2$ into the first equation:** $$ 2(-2) - y = 7 $$ $$ -4 - y = 7 $$ $$ -y = 11 $$ $$ y = -11 $$ 6. **Step 4: Conclusion:** - The system has a unique solution $(x,y) = (-2, -11)$. - Therefore, the system is **consistent** and **independent**. Final answer: The system is consistent and independent with solution $$\boxed{(-2, -11)}$$.