Question

If (p, p) is the solution of system of equations ax + by + (t – s) = 0 and bx + ay + (s – r) = 0, (a ≠ b) then which of the following must be true ?

A) 2s = r + t 

B) r + s + t = 0 

C) 2r = s + t 

D) 2t = r + s

Answer 1

Correct option is (A) 2s = r + t

Given that (p, p) is the solution of system of equations ax + by + (t – s) = 0

and bx + ay + (s – r) = 0

\(\therefore\) ap + bp + t - s = 0    ____________(1)

bp + ap + s - r = 0       ____________(2)

Subtract equation (1) from (2), we get

(ap + bp + s - r) - (ap + bp + t - s) = 0 - 0 = 0

\(\Rightarrow\) s - r - t + s = 0

\(\Rightarrow\) 2s - r - t = 0

\(\Rightarrow\) 2s = r + t

Answer 2

Correct option is A) 2s = r + t