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Question
Solve for x and y:
px + qy = p – q,
qx – py = p + q
Solution
The given equations are
px + qy = p – q ………(i)
qx – py = p + q ………(ii)
Multiplying (i) by p and (ii) by q and adding them , we get
`p^2x + q^2x = p^2 – pq + pq + q^2`
`x = (p^2+ q^2)/(p^2+ q^2) = 1`
Substituting x = 1 in (i), we have
p + qy = p – q
⇒qy = -p
⇒y = -1
Hence, x = 1 and y = -1.
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