Asked by a
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
minus, 5, x, plus, y, equals, 7
−5x+y=
7
5, x, minus, y, equals, minus, 5
5x−y=
−5
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Answered by
GPT-5 mini
AI
No solutions.
Add the two equations: (-5x + y) + (5x − y) = 7 + (−5) ⇒ 0 = 2, a contradiction. The lines are parallel (same left side, different constants), so the system is inconsistent.
Add the two equations: (-5x + y) + (5x − y) = 7 + (−5) ⇒ 0 = 2, a contradiction. The lines are parallel (same left side, different constants), so the system is inconsistent.
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