Question

Write the condition for which the pair of liner

equations a1

x + b1

y + c1

= 0, a2

x + b2

y + c2

= 0

said to be inconsistent. ​

Answer 1

Answer:

a1/a2 equal to b1 / b2 not equal to c1/c2.

this is the condition for the equations to be inconsistent

Answer 2

Given :  a1x + b1y + c1= 0  , a2x + b2y + c2= 0

To Find : Condition for Equations to be  inconsistent. ​

Solution:

a1x + b1y + c1= 0

a2x + b2y + c2= 0

Given two lines would be inconsistent if

a1/a2 = b1/b2  ≠ c1/c2

Lines Inconsistent means that lines Does not have any mutual Solution

means line are parallel to each other and does not intersect each other

if  a1/a2 = b1/b2  = c1/c2  - Consistent

then both lines are basically the same and hence has infinite solutions

if a1/a2 ≠ b1/b2   - Consistent

and have one mutual solution  where lines intersect each other

a1/a2 = b1/b2  ≠ c1/c2  is the condition for the pair of lines to be inconsistent

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