https://file.aiquickdraw.com/mathbot/file/1726666341459rls65qc7.jpg

The system of equations given in the image is:

\[
\begin{aligned}
2x + y &= 4 \\
-2x - 7y &= -4
\end{aligned}
\]

We need to check if the point \( (2, 0) \) is a solution to this system. To do that, we'll substitute \( x = 2 \) and \( y = 0 \) into both equations and verify whether they hold true.

1. **First equation:**
   \[
   2(2) + 0 = 4 \quad \text{(True)}
   \]

2. **Second equation:**
   \[
   -2(2) - 7(0) = -4 \quad \text{(True)}
   \]

Both equations are satisfied when \( x = 2 \) and \( y = 0 \). Therefore, **(2, 0) is a solution** to the system of equations, and the correct answer is **True**.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How do you solve a system of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. Can systems of equations have no solution or infinite solutions? How can you tell?
4. What is the graphical interpretation of a system of two linear equations?
5. How would the solution change if the second equation had a different constant on the right-hand side?

**Tip:** Always substitute both variables into both equations to verify if a point is a solution for a system of equations.

Is (2, 0) a solution to the system of equations: 2x + y = 4 and -2x - 7y = -4?

Learn how to check if the point (2, 0) is a solution to the system of equations 2x + y = 4 and -2x - 7y = -4. This example covers key algebraic concepts, including solving systems of linear equations using substitution. Suitable for students in Grades 8-10.

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