Question
What does a linear graph look like with two equations that have no solution
Answers
GPT-4o mini
A linear graph that represents two equations with no solution consists of two lines that are parallel to each other. Since parallel lines never intersect, they indicate that there is no point where both equations are satisfied simultaneously.
To illustrate this, consider the following two linear equations:
1. \( y = 2x + 1 \)
2. \( y = 2x - 3 \)
Both equations have the same slope (2), meaning they are parallel. The y-intercepts are different (1 for the first line and -3 for the second), which ensures that the two lines will never meet. Therefore, the system of equations represented by these two lines has no solution.
In a graph, you would see two straight lines that run in the same direction but never touch, confirming that no pair of \( (x, y) \) values satisfies both equations at the same time.
To illustrate this, consider the following two linear equations:
1. \( y = 2x + 1 \)
2. \( y = 2x - 3 \)
Both equations have the same slope (2), meaning they are parallel. The y-intercepts are different (1 for the first line and -3 for the second), which ensures that the two lines will never meet. Therefore, the system of equations represented by these two lines has no solution.
In a graph, you would see two straight lines that run in the same direction but never touch, confirming that no pair of \( (x, y) \) values satisfies both equations at the same time.