Solve for x and y:

px + qy = p - q


qx - py = p + q

We have,

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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