Using the techniques discussed in this section, solve the following system of linear equations. Enter the solution as an ordered pair. For parametric solutions use 
x = t
 as the parameter. (If an answer does not exist, enter DNE.)
 

−10x	 − 	14y	 = 	3
−5x	 − 	7y	 = 	−7


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.

Using the techniques discussed in this section, solve the following system of linear equations. Enter the solution as an ordered pair. For parametric solutions use x = t as the parameter. (If an answer does not exist, enter DNE.)

−10x − 14y = 3
−5x − 7y = −7

Learn how to solve a system of linear equations using the elimination method. This example demonstrates an inconsistent system with no solution, guiding you through each step to reach the conclusion DNE (Does Not Exist). Perfect for students in Grades 9-11 studying algebra and systems of equations.

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