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

(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.