Math Problem Statement
Solution
The correct graph is marked as B in the image. Here's how we can interpret why:
- A system of linear equations is represented by two lines on the graph, and the point where these lines intersect represents the solution to the system.
- In option B, the two lines intersect at a single point, which indicates a system of linear equations that has one unique solution.
- The other graphs either show parallel lines (indicating no solution, as they never intersect) or lines that overlap (indicating infinitely many solutions, since the lines coincide).
In the case of graph B, the lines are neither parallel nor coinciding, but they intersect at a distinct point, making it the correct representation of Sabrina's system of equations.
Would you like more details on how to graph systems of equations or analyze the intersections?
Here are five related questions to consider:
- What does it mean for a system of equations to have no solution?
- How do you find the point of intersection for two lines algebraically?
- What is the difference between dependent and independent systems?
- How can you determine the slope of a line by looking at a graph?
- What are the characteristics of parallel lines in terms of their slopes?
Tip: To check if two lines will intersect, compare their slopes—if the slopes are different, the lines will intersect at a point.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Graphing
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b
Theorems
Theorem of Linear Systems (Unique, No Solution, or Infinite Solutions)
Suitable Grade Level
Grades 8-10