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.