px+qy=p-q and qx-py=p+q. Solve this Simultaneous Linear Equations by Elimination Method.[ICSE ML Aggarwal Class 9 Chapter 5 Exercise-5.2 Question 9(i) Solution ]
px+qy=p-q —-(i)
qx-py=p+q —-(ii)
Multiplying Equation (i) by p and Equation (ii) by q we get,
p2x+pqy=p2-pq —-(iii)
q2x-pqy=pq+q2 —-(iv)
Adding (iii) and (iv) we get,
(p2x+pqy)+(q2x-pqy)=(p2-pq)+(pq+q2 )
⟹ p2x+pqy +q2x-pqy=p2-pq+pq+q2
⟹ p2x +q2x =p2 + q2
⟹ x(p2+q2)=p2 + q2
⟹ x =$\frac{{\mathrm{p}}^2 + {\mathrm{q}}^2}{{\mathrm{p}}^2 + {\mathrm{q}}^2}$
⟹ x =1
Now from equation (i) we get,
p(1)+qy=p-q
⟹ p +qy=p-q
⟹ qy= -q
⟹ y = $\frac{ – {\mathrm{q}}}{{\mathrm{q}}}$
⟹ y=-1
Therefore Required Solutions are x = 1 and y = -1