https://file.aiquickdraw.com/mathbot/file/1725875553115ighumabd.jpg

The graph shows two distinct lines intersecting at a single point. In terms of linear equations, this scenario corresponds to a "consistent system" with a "unique solution."

- Two linear equations are **consistent** if they have at least one common solution.
- A system with a **unique solution** means the two lines intersect at exactly one point, which we observe in the graph.

Thus, the correct answer is **(a) Consistent with unique solution**.

Would you like more details on how to interpret linear systems graphically?

Here are five questions related to this problem:

1. How can you determine if two lines are parallel by looking at their equations?
2. What does it mean for a system of equations to be inconsistent?
3. How can you tell if a system of equations has infinitely many solutions?
4. What is the significance of the slopes in determining the number of solutions of a system?
5. How does the point of intersection relate to the solution of the system of equations?

**Tip:** When lines intersect at a single point, it represents the only solution that satisfies both equations simultaneously.

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:

Explore the concept of a consistent system with a unique solution by analyzing the intersection of two linear equations on a graph. Learn how the point of intersection represents the only solution to the system. Suitable for students in Grades 8-10.

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