Math Problem Statement

Which graph best represents a system of equations that has no solution?

Solution

To determine which graph represents a system of equations with no solution, we need to identify parallel lines. Parallel lines never intersect, meaning the system has no solution. Parallel lines have the same slope but different y-intercepts.

Analyzing the graphs:

  • Graph A: The lines intersect at one point, meaning the system has one solution.
  • Graph B: The two lines are parallel, as they have the same slope but different y-intercepts. This is a system with no solution.
  • Graph C: The lines intersect at one point, meaning the system has one solution.
  • Graph D: The lines intersect at one point, meaning the system has one solution.

Correct Answer: B

Let me know if you want further clarification or additional questions. Here are 5 related questions for further exploration:

  1. How do you calculate the slope of a line from a graph?
  2. What are the characteristics of systems with infinite solutions?
  3. Can two lines with different slopes ever be parallel? Why or why not?
  4. What is the significance of the y-intercept in determining the solution to a system of equations?
  5. How can you algebraically determine if a system of equations has no solution?

Tip: Always compare the slopes of the lines to quickly determine if they are parallel (same slope) or intersecting (different slopes).

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Parallel Lines

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Parallel lines have equal slopes but different y-intercepts

Suitable Grade Level

Grades 8-10