Math Problem Statement
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:
- What do parallel lines in a system of equations signify?
- How can you determine the solution of a system by graphing?
- What are the possible types of solutions for a system of two linear equations?
- How would you write the system of equations for Graph A?
- 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