Math Problem Statement

Which graph represents the system and its solution?

Solution

The image shows four graphs (A, B, C, D) plotting "3 Point Shots" on the y-axis and "2 Point Shots" on the x-axis. The task is to identify which graph represents the system of linear equations and its solution.

Looking closely at the graphs:

  • Graph A: The two lines intersect at a single point, indicating a solution to the system.
  • Graph B: The lines cross each other, indicating a solution, but the configuration suggests inconsistent scales or behaviors.
  • Graph C: The lines are parallel, which indicates no solution, as parallel lines never intersect.
  • Graph D: The lines intersect at a point, indicating one solution to the system.

Based on this analysis, Graph A represents the system and its solution because it shows two lines intersecting at a single point, which is the correct behavior for a system with one solution.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

  1. What do parallel lines in a system of equations signify?
  2. How can you determine the solution of a system by graphing?
  3. What are the possible types of solutions for a system of two linear equations?
  4. How would you write the system of equations for Graph A?
  5. What is the significance of the intersection point in a system of equations?

Tip: Always check if the lines in a system are parallel to determine if there’s no solution!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Systems
Graphing Equations

Formulas

Slope-intercept form of a line: y = mx + b
Solving systems of equations by graphing

Theorems

The intersection of two lines represents the solution to a system of equations
Parallel lines have no solution

Suitable Grade Level

Grades 8-10