Math Problem Statement

Refer to the illustration. Answer the questions.

How many solutions does the system of equations have? Are the equations dependent or independent?

one solution, independent equations

two solutions, independent equations

infinite number of solutions, dependent equations

no solution, independent equations

no solution, dependent equations

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? Are the equations dependent or independent?

Solution

The image shows two lines on a coordinate plane: one blue line and one pink line. They intersect at exactly one point. Based on this visual information, let's analyze the system of equations represented by these two lines.

  • Number of solutions: Since the two lines intersect at exactly one point, the system has one solution.
  • Dependence or independence: Since the lines are not parallel and intersect at one point, the equations are independent.

Answer:

  • One solution, independent equations.

Would you like more details, or do you have any questions?

Related Questions:

  1. How can you determine if two lines are parallel or perpendicular from their equations?
  2. What is the slope of the blue line and the pink line in the graph?
  3. How do you find the point of intersection of two lines algebraically?
  4. What is the significance of independent equations in a system of linear equations?
  5. How does the concept of dependent equations relate to the slopes of the lines?

Tip: Two lines are independent if they have different slopes, ensuring they intersect at one point.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Coordinate Geometry

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

Intersection of lines
Unique solution theorem for linear equations

Suitable Grade Level

Grades 9-11