Question
Sun August 05, 2012 By: Nilesh Raikar
 

(p-q)x = (p+q)y and px-2y=r . find the condition for which the following system of equation will be inconsistent

Expert Reply
Sun August 05, 2012
(p-q)x = (p+q)y
(p-q)x - (p+q)y = 0          ... (1)
 
px - 2y - r = 0                  ... (2)
 
The given system of equation will be inconsistent if a1/a2 = b1/b2 not equals c1/c2
 
(p-q) / p = -(p + q) / -2 not equal to 0            (Since, c1 = 0)
 
First and last equality gives p not equal to q
Second and last equality gives p not equal to -q
First and second equations give
(p-q) / p = (p + q) /2 
Simplify this to get the third conditions,
 
Thus, the given system of equations will be inconsistent if the above three conditions hold.
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