px+qy=p-q and qx-py=p+q. Solve this Simultaneous Linear Equations by Elimination Method.

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