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What is the classification of each system?

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{4x+y=8x+3y=8
{−4x+6y=−22x−3y=1
{5x−2y=45x−2y=6

1 answer

Based on the given systems of equations, here’s the classification:

  1. System 1:

    • Equations:
      • \(4x + y = 8\)
      • \(3y = 8\)
    • Classification: Inconsistent (These equations represent parallel lines that never intersect.)

  2. System 2:

    • Equations:
      • \(-4x + 6y = -2\)
      • \(2x - 3y = 1\)
    • Classification: Independent (These equations represent lines that intersect at exactly one point.)

  3. System 3:

    • Equations:
      • \(5x - 2y = 4\)
      • \(5x - 2y = 6\)
    • Classification: Inconsistent (These equations also represent parallel lines that never intersect.)

To match the classifications to each system:

  • System 1: Inconsistent
  • System 2: Independent
  • System 3: Inconsistent

Make sure to drag the correct classifications into their respective boxes!