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

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Solve the pair of linear equations:

px + qy = p – q

qx – py = p + q

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px + qy = p – q……………(i)

qx – py = p + q……………….(ii)

Multiplying p to equation (1)  and q to equation (2), we get

p2x + pqy = p2 − pq ………… (iii)

q2x − pqy = pq + q2 ………… (iv)

Adding equation (iii) and equation (iv),we get

p2x + q2 x = p2  + q2

(p2 + q2 ) x = p2 + q2

x = (p2 + q2)/ p2 + q= 1

From equation (i), we get

p(1) + qy = p – q

qy = p-q-p

qy = -q

y = -1

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