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To determine if the ordered pair \((0,0)\) is a solution to the given system of linear equations, we can substitute \(x = 0\) and \(y = 0\) into each equation and check if both equations are satisfied.

The system of equations is:
\[
2x + y = 0
\]
\[
-x + 2y = 5
\]

### Step 1: Substitute \(x = 0\) and \(y = 0\) into the first equation
\[
2(0) + 0 = 0
\]
\[
0 = 0
\]
This is true, so the first equation is satisfied.

### Step 2: Substitute \(x = 0\) and \(y = 0\) into the second equation
\[
-0 + 2(0) = 5
\]
\[
0 = 5
\]
This is false, so the second equation is not satisfied.

### Conclusion
The ordered pair \((0,0)\) does **not** satisfy the second equation, so it is **not a solution** to the system of equations.

Would you like further details or have any questions?

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Here are five related questions for further exploration:
1. What are the conditions required for a pair to be a solution to a system of equations?
2. How can you solve a system of linear equations if substitution fails?
3. What are graphical methods for finding solutions to systems of equations?
4. How do you determine if a system of equations is consistent or inconsistent?
5. What is the difference between independent, dependent, and inconsistent systems?

**Tip:** When verifying solutions, remember to substitute the values into **all** equations in the system. If they satisfy every equation, then they are a solution.

Tell whether the ordered pair (0,0) is a solution of the system of linear equations: 2x + y = 0 and -x + 2y = 5. Substitute 0 for x and 0 for y in each equation and solve.

Verify if the ordered pair (0,0) is a solution to the system of equations 2x + y = 0 and -x + 2y = 5. This exercise covers algebra concepts related to linear systems and solution verification. Suitable for students in Grades 8-10.

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