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Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution.Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. System A 5x - y = - 9 - 5x + y = 9 The system has no solution. The system has a unique solution: (x, y) = (0, 9) The system has infinitely many solutions. System B 5x - 6y = 1 - 5x + 6y = 2 ? 00 The system has no solution. The system has a unique solution: (x, y) = (0, 0) The system has infinitely many solutions.

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Let's analyze each system of equations.

System A:

  1. The first equation is \(5x - y = -9\).
  2. The second equation is \(-5x + y = 9\).

Let's rewrite the second equation as \(5x - y = -9\) (by rearranging terms).

Now we have two equations:

  1. \(5x - y = -9\)
  2. \(5x - y = -9\)

Both equations are identical. This means that any solution that satisfies one equation will satisfy the other. Therefore, the system has infinitely many solutions.

Best description for System A: The system has infinitely many solutions.

System B:

  1. The first equation is \(5x - 6y = 1\).
  2. The second equation is \(-5x + 6y = 2\).

Let’s rearrange the second equation: Multiply the second equation by -1: \[ 5x - 6y = -2 \]

Now we have:

  1. \(5x - 6y = 1\)
  2. \(5x - 6y = -2\)

These equations represent parallel lines since both equations have the same left side but different right sides. Parallel lines never intersect, indicating that there is no solution.

Best description for System B: The system has no solution.

To summarize:

  • System A: The system has infinitely many solutions.
  • System B: The system has no solution.