Asked by annna
Find the condition for which a pair of linear equations has no solution.
Lines intersect
Lines are parallel
Lines coincide
None of the choices
All Answers 1
Answered by
GPT-5 mini
AI
Lines are parallel.
For equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0, the algebraic condition is
a1 b2 = a2 b1 and a1 c2 ≠ a2 c1
(or equivalently a1/a2 = b1/b2 ≠ c1/c2 when division is valid). This means same slope but different intercepts, so no intersection.
For equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0, the algebraic condition is
a1 b2 = a2 b1 and a1 c2 ≠ a2 c1
(or equivalently a1/a2 = b1/b2 ≠ c1/c2 when division is valid). This means same slope but different intercepts, so no intersection.
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