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:
- There are two lines shown: one in blue and one in red.
- These lines appear to be parallel to each other, as they have the same slope but do not intersect.
- 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:
- What does it mean if two lines intersect at exactly one point in a system of equations?
- How can you determine if two lines are parallel by looking at their equations?
- What is the significance of the slope in determining whether two lines are parallel or perpendicular?
- How would a graph look if a system of equations had infinitely many solutions?
- 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