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The problem asks to find which ordered pair is the solution to the following system of linear equations:

\[
3x + 4y = -10
\]
\[
2x - 4y = 0
\]

We can solve this system step by step using substitution or elimination. Let's go ahead and solve it using elimination.

### Step 1: Add the two equations
If we add the two equations together, the \(4y\) and \(-4y\) terms will cancel out:

\[
(3x + 4y) + (2x - 4y) = -10 + 0
\]
This simplifies to:
\[
5x = -10
\]

### Step 2: Solve for \(x\)
Now divide both sides by 5:
\[
x = \frac{-10}{5} = -2
\]

### Step 3: Substitute \(x = -2\) into one of the original equations
We can substitute \(x = -2\) into the second equation \(2x - 4y = 0\):

\[
2(-2) - 4y = 0
\]
This simplifies to:
\[
-4 - 4y = 0
\]

### Step 4: Solve for \(y\)
Now solve for \(y\):

\[
-4y = 4
\]
\[
y = \frac{4}{-4} = -1
\]

### Solution:
The solution to the system is \(x = -2\) and \(y = -1\), or \((-2, -1)\).

### Conclusion:
The correct answer is **C**: \((-2, -1)\).

---

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions for practice:
1. Solve the system of equations: \(x + y = 5\) and \(x - y = 1\).
2. If you change the system to \(3x + 4y = 10\) and \(2x - 4y = 4\), what is the solution?
3. Solve by substitution: \(4x + y = 9\) and \(x - y = 1\).
4. How do you determine if a system of equations has no solution or infinite solutions?
5. What happens when you solve a system of equations that are both multiples of each other?

**Tip:** In linear systems, elimination is particularly useful when variables can easily be canceled out by adding or subtracting equations!

Which ordered pair is the solution of the linear system 3x + 4y = -10 and 2x - 4y = 0?

Learn how to solve the system of linear equations 3x + 4y = -10 and 2x - 4y = 0 using the elimination method. This step-by-step guide is designed for students in Grades 8-10.

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