Write the condition for the given system of equations to be inconsistent.
a1x + b1y + c1 = 0, a2x + b2y + c2 = 0


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Answer:

 

a1
a2
  =  
b1
b2
  ≠  
c1
c2
 

Step by Step Explanation:
  1. A pair of equations is said to be inconsistent if no solution exists that can satisfy both the equations.
  2. A pair of equations would have no solution if the ratio of coefficients of variables is same but is different from the ratio of the constants, i.e.
     
    a1
    a2
      =  
    b1
    b2
      ≠  
    c1
    c2
      ,
    where a1, b1 and a2, b2 are the coefficients of the variables and c1 and c2 are the constants of the equations respectively.
  3. Hence, the condition for the given pair of equations to be inconsistent is  
    a1
    a2
      =  
    b1
    b2
      ≠  
    c1
    c2
     .

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