Math Problem Statement

Which statement about this system of equations is true?

Solution

To determine the correct answer to this question, let's analyze the graph provided:

  1. There are two lines shown: one in blue and one in red.
  2. These lines appear to be parallel to each other, as they have the same slope but do not intersect.
  3. When two lines are parallel and do not intersect, it means the system of equations they represent has no solution (they never meet at any point).

Conclusion:

The correct answer is: A. The system has no solution.

Would you like a more detailed explanation or have any questions on this topic?


Here are some related questions to explore:

  1. What does it mean if two lines intersect at exactly one point in a system of equations?
  2. How can you determine if two lines are parallel by looking at their equations?
  3. What is the significance of the slope in determining whether two lines are parallel or perpendicular?
  4. How would a graph look if a system of equations had infinitely many solutions?
  5. How do you write the equations for lines that are parallel to each other?

Tip: For a system of equations, if two lines have the same slope but different y-intercepts, they are parallel and have no solutions.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Parallel Lines
Systems of Equations

Formulas

Slope-Intercept Form y = mx + b

Theorems

Parallel Lines in a Plane

Suitable Grade Level

Grades 8-10