Q. 424.1( 14 Votes )
Solve for x and y:
px + qy = p - q
qx - py = p + q
px + qy = p – q …(i)
qx – py = p + q …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply equation (i) by p and (ii) by q, so that variable y in both the equations have same coefficient.
Recalling equations (i) & (ii),
px + qy = p – q [×p]
qx – py = p + q [×q]
⇒ p2x + q2x = p2 + q2
⇒ (p2 + q2)x = p2 + q2
⇒ x = 1
Substitute x = 1 in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (i), we get
p + qy = p – q
⇒ qy = - q
⇒ y = - 1
Hence, we have x = 1 and y = - 1.
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