Solve the following pair of linear equations:(i) px + qy = p - q; qx - py = p + q (ii) ax + by = c; bx + ay = 1 + c

(i)px+qy=p−q…(i)qx−py=p+q…(ii)Multiplying(i)by p and(ii)byqwe get(iii)and(iv)respectively asp2x+pqy=p2−pq…(iii)q2x−pqy=pq+q2…(iv)Adding(iii)and(iv)we get,(p2+q2)x=(p2+q2)⇒x=1Substituting value ofxin(i), we getp+qy=p−qqy=−qy=−1;Hence,x=1,y=−1;(ii)ax+by=c…(i)bx+ay=1+c…(ii)Multiplying(i)byband(ii)by a we get(iii)and(iv)respectively asabx+b2y=bc…(iii)abx+a2y=a+ac…(iv)Subtracting(iv)from(iii), we get(b2−a2)y=(b−a)c−ay=(b−a)c−a(b2−a2)Substituting value ofyin(i), we getax+b×(b−a)c−a(b2−a2)=cax=c−(b−a)bc−ab(b2−a2)ax=c(b2−a2)−b2c+abc+ab(b2−a2)x=cb2−ca2−b2c+abc+aba(b2−a2)x=ab+abc−ca2a(b2−a2)x=b−bc−ca(b2−a2)x=b+c(b−a)(b2−a2)