We are given the system of linear equations:

$-10x - 14y = 3 \quad \text{(Equation 1)}$ $-5x - 7y = -7 \quad \text{(Equation 2)}$

Step 1: Simplify the second equation

Notice that the second equation can be rewritten by multiplying it by 2:

$2(-5x - 7y) = 2(-7)$ $-10x - 14y = -14 \quad \text{(Equation 3)}$

Step 2: Compare equations

Now we have:

$-10x - 14y = 3 \quad \text{(Equation 1)}$ $-10x - 14y = -14 \quad \text{(Equation 3)}$

Step 3: Analyze the system

Equations 1 and 3 are inconsistent. On the left-hand side, both equations are identical, but the right-hand sides are different ($3 \neq -14$).

Conclusion:

Since the two equations are inconsistent, the system has no solution. Therefore, the answer is DNE (Does Not Exist).

Would you like more details, or do you have any questions?

Here are five related questions to expand on this:

1. How do you solve systems of linear equations using substitution?
2. What is the graphical interpretation of an inconsistent system of equations?
3. How does the elimination method work for solving systems of linear equations?
4. What is the difference between a consistent and inconsistent system of equations?
5. How do parametric solutions apply to systems with infinite solutions?

Tip: Always check if the system is consistent or inconsistent before proceeding to solve, as it can save time on unnecessary calculations.