A system of two linear equations has no solutions. What must be true about their graphs in the xy-plane?

Answer and explanation

Correct answer: B. The lines are parallel and distinct

  1. Step 1: A system of linear equations has no solutions if and only if the lines never intersect.
  2. Step 2: In Euclidean geometry, two lines that never intersect in the same plane are parallel and distinct (identical slopes, different y-intercepts).
Answer
The lines are parallel and distinct.
Why not the others: 'The lines intersect at a right angle' yields exactly one solution; 'The lines are identical' yields infinitely many solutions; 'Opposite reciprocal slopes' describes perpendicular lines with one solution.

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