Question

what is the condition that the pair of linear equation ax+by+c=0and Ax+By+C=0 is consistent?​

Answer 1

Given  : the pair of linear equation ax+by+c=0 and Ax+By+C=0

To Find : condition that the pair of linear equation  is consistent ​

Solution:

pair of linear equation

ax+by+c=0  

Ax+By+C=0

Consistent   and unique solution ( intersecting line)

a/A  ≠ b/B

Consistent   and Infinite  solution ( same line)

a/A = b/B = c/C

Inconsistent and no solution ( Parallel lines)

a/A = b/B ≠ c/C

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