What will be the condition of lines if a pair of linear equations is consistent?

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Mamata Mund

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Consistent with unique solution -( a1/a2 ) not equal to (b1/b2) coincident -( a1/a2) = (b1/b2)=(c1/c2)
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Math Magician

Algebraically, if a1/a2 & b1/b2 then, the linear equations’ pair is consistent. If a1/a2 = b1/b2 = c1/c2 we can say that the above equations represent lines which are coincident in nature and the pair of equations is dependent and consistent.
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Gourav Khandelwal

For two lines to be coincident the two equations say, a1x+b1y+c1= 0 = a2x+b2y+c2 must follow the the following property: (a1/a2) = (b1/b2) = (c1/c2)
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Maths Teacher

There are three conditions for a pair of lines: 1. The two lines intersect at a point, then there is a unique solution and hence the pair of linear equations is consistent 2. If the lines coincide and hence there are infinite number of solutions. And the equations are dependent 3. If the lines are parallel,...
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There are three conditions for a pair of lines: 1. The two lines intersect at a point, then there is a unique solution and hence the pair of linear equations is consistent 2. If the lines coincide and hence there are infinite number of solutions. And the equations are dependent 3. If the lines are parallel, there is no solution, because parallel lines never intersect. If the pair of equations is having at least one solution, then the system is said to be consistent Therefore, from the above cases, 1 and 2 are said to be consistent. read less
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