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Which of the following describes a dependent system of linear equations?

Practice Questions

Q1
Which of the following describes a dependent system of linear equations?
  1. The equations have no solutions.
  2. The equations have exactly one solution.
  3. The equations have infinitely many solutions.
  4. The equations are parallel.

Questions & Step-by-Step Solutions

Which of the following describes a dependent system of linear equations?
  • Step 1: Understand what a system of linear equations is. It is a set of two or more equations with the same variables.
  • Step 2: Know that a dependent system means the equations are not independent; they are related.
  • Step 3: Realize that if two equations represent the same line, they will have the same slope and y-intercept.
  • Step 4: Recognize that if the equations are the same line, they will have infinitely many solutions because every point on the line is a solution.
  • Step 5: Conclude that a dependent system of linear equations is one where the equations represent the same line, leading to infinitely many solutions.
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