Math Problem Statement
Solution
In this image, the question asks, "Which graph represents the system Sabrina graphed?" There are four graphs labeled A, B, C, and D, showing various systems of linear equations (two lines each).
Looking at graph C, which is marked as the selected answer:
- Graph C shows two lines that intersect at the point (2, 4), suggesting a solution to the system of equations.
- Both lines are distinct and appear to have different slopes, which is a common representation of two linear equations with a single point of intersection (meaning the system has one unique solution).
The system of equations most likely graphed by Sabrina has this solution at (2, 4), confirming that graph C is the correct answer.
Would you like details on how to find the equations of these lines, or do you have any questions?
Here are 5 relative questions to expand your understanding:
- How can you derive the equations of the lines from the graph?
- What does the slope of a line represent, and how is it calculated from a graph?
- How can you determine the solution of a system of equations from a graph?
- What does it mean if two lines in a system of equations are parallel?
- What does it mean if two lines in a system coincide (overlap)?
Tip: To solve a system of linear equations graphically, always look for the point where the lines intersect. That point gives the solution to the system!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Graphing
Formulas
Slope Formula: (y2 - y1) / (x2 - x1)
Equation of a Line: y = mx + b
Theorems
Point of Intersection as a Solution
Suitable Grade Level
Grades 8-10