Q) Solve the following pair of linear equations:
px + qy = p – q
qx – py = p + q

Ans: 

Given the equations:

Solve the following pair of linear equations:
px + qy = p – q …………. (i)
qx – py = p + q ………….. (ii)

Let’s multiply equation (i) with p and equation (ii) with q and we get:

p² x + pq y = p² – pq  

q² x – pq y = pq + q²

Let’s add these 2 equations:

p² x + q² x  = p² + q²

∴ x (p² + q² ) = p² + q²

∴ x = 1

Let’s put x = 1 in equation (i), we get:

p (1) + qy = p – q

∴ qy = – q

∴ y = – 1 

Therefore, x = 1 and y = – 1  

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