Question

if (1,1) is the solution of the equation px + qy + (a-b) = 0 and px + qy + (b-c) = 0 then find a+c​

Answer 1

Given :  (1,1) is the solution of the equation px+qy+(a-b)=0 and px+qy+(b-c)=0  

To Find : a+c

Solution:

px+qy+(a-b)=0  

(1,1) is the solution

=> p + q  + (a - b)  = 0  

px+qy+(b-c)=0  

(1,1) is the solution

=> p + q + ( b - c)  = 0

Equating both

p + q  + (a - b)   =   p + q + ( b - c)

=> a - b  = b  - c

=> a + c  = 2b

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