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The problem asks to find the solution of the linear system:

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

To solve this system, we can use the elimination method.

### Step 1: Add the two equations
First, we add the equations to eliminate \(y\). Notice that the coefficients of \(y\) are opposites, so adding the two equations will cancel \(y\).

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

### Step 2: Solve for \(x\)
Now, solve for \(x\):
\[
x = \frac{-10}{5} = -2
\]

### Step 3: Substitute \(x = -2\) into one of the original equations
Substitute \(x = -2\) into the first equation, \(3x + 4y = -10\):

\[
3(-2) + 4y = -10
\]
\[
-6 + 4y = -10
\]

### Step 4: Solve for \(y\)
Now, solve for \(y\):
\[
4y = -10 + 6
\]
\[
4y = -4
\]
\[
y = \frac{-4}{4} = -1
\]

### Conclusion:
The solution to the system is \(x = -2\) and \(y = -1\), which corresponds to the ordered pair \((-2, -1)\).

Thus, the correct answer is **C**.

Would you like more details on any part of the solution?

Here are some related questions for practice:
1. How do you solve a linear system using the substitution method?
2. What is the graphical interpretation of solving a system of linear equations?
3. Can you always solve a system of linear equations by adding or subtracting the equations?
4. What is the difference between consistent and inconsistent systems of equations?
5. How do you solve a system of equations using the matrix method?

**Tip:** When using the elimination method, always check if adding or subtracting the equations will help cancel one variable, simplifying the solution process.

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 solution is designed for students in Grades 8-10.

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