Aaron wrote the function 5x+3y=‒9
as the first equation in a system of equations. He then graphed the second equation on the coordinate plane.

Which statement is true about the solution to the system of equations?
A.The system has no solutions.
B.The system has exactly one solution.
C.The system has exactly two solutions.
D.The system has infinitely many solutions.

The given equation is:

\[
5x + 3y = -9
\]

This represents a straight line. To determine the solution to the system of equations, we need to consider the second equation and how it interacts with this first equation when plotted on the coordinate plane.

- If the two lines are **parallel** (same slope but different y-intercepts), the system will have **no solutions** (option A), as the lines never intersect.
- If the two lines **intersect at one point**, the system will have **exactly one solution** (option B).
- If the two lines **coincide** (are the same line), the system will have **infinitely many solutions** (option D).
- There cannot be exactly two solutions (option C) for a system of linear equations, since two lines either do not intersect, intersect at one point, or coincide entirely.

Since no details about the second equation are provided, we cannot definitively determine the type of solution without more information about that second line. However, typically, linear systems have **one solution** unless they are parallel or the same line.

Thus, if no additional information suggests otherwise, **option B** ("The system has exactly one solution") is most likely the correct answer, assuming the second equation represents a line that intersects the first at exactly one point.

Would you like more details or have any further questions? Here are some related questions to explore:

1. What happens when two lines have the same slope but different y-intercepts?
2. How do you calculate the point of intersection between two lines?
3. What are the conditions for two lines to be parallel?
4. What does it mean when two equations are dependent?
5. Can two lines intersect at more than one point?

**Tip:** When dealing with systems of equations, always compare the slopes and intercepts to determine how the lines behave relative to each other.

Aaron wrote the function 5x + 3y = -9 as the first equation in a system of equations. He then graphed the second equation on the coordinate plane. Which statement is true about the solution to the system of equations? A. The system has no solutions. B. The system has exactly one solution. C. The system has exactly two solutions. D. The system has infinitely many solutions.

Learn how to determine the solution of a system of equations, including 5x + 3y = -9, and explore different cases like parallel lines, intersection points, and coincident lines. This problem is ideal for students in Grades 8-10, covering key concepts in algebra and graphing.

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