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consider the given system of equations. how many (x,y) soul does this system have?

Let's consider the system of equations shown in the image:

\[
2x + 4y = 15
\]
\[
2x + 4y = 13
\]

Both equations have the same left-hand side (i.e., \(2x + 4y\)), but the right-hand sides are different. This means the system is **inconsistent**, because \(2x + 4y\) cannot equal both 15 and 13 at the same time.

Therefore, this system of equations has **no solutions**.

The correct answer is:
- \( \text{A) No solutions} \)

Would you like further clarification or details? 

Here are five related questions:
1. What does it mean for a system of equations to have "exactly one solution"?
2. How do you determine if two equations represent parallel lines?
3. What is the graphical interpretation of a system with no solutions?
4. How do you algebraically identify whether a system has infinitely many solutions?
5. Can a system with different coefficients still have no solutions?

**Tip:** When two linear equations in a system have the same left-hand side but different constants on the right-hand side, they represent parallel lines, which never intersect, meaning there are no solutions.

Consider the given system of equations. How many (x,y) solutions does this system have?

This problem explores a system of linear equations with no solutions. Learn why the system is inconsistent and how parallel lines explain the result. Suitable for students in Grades 9-11 studying Algebra.

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