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To solve the system of equations:

1. \(-4x - 6y = 6\)
2. \(4x + 6y = -4\)

We can approach this using the elimination method, as the coefficients of both \(x\) and \(y\) are the same in magnitude but opposite in sign. Let's add the two equations together to eliminate both variables:

\[
(-4x - 6y) + (4x + 6y) = 6 + (-4)
\]
\[
0 = 2
\]

Since we end up with a false statement \(0 = 2\), this system of equations has no solution.

Thus, the correct answer is **"no solution."**

Would you like further explanation, or do you have any questions?

Here are 5 related questions to explore:
1. What does it mean if a system of equations has infinitely many solutions?
2. How do you solve a system of equations using substitution instead of elimination?
3. What are the conditions for a system of equations to have no solution?
4. How can you graphically represent a system of linear equations with no solution?
5. How does solving a system of nonlinear equations differ from solving linear ones?

**Tip:** In elimination, always check if adding or subtracting the equations simplifies both variables—this helps identify unique, no, or infinite solutions quickly!

Solve the system: -4x - 6y = 6 and 4x + 6y = -4

Learn how to solve the system of linear equations -4x - 6y = 6 and 4x + 6y = -4 using the elimination method. This problem illustrates the concept of a system with no solution, where the lines are parallel and never intersect. Suitable for students in Grades 8-10.

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