 Hello and welcome to the session. Let us understand the following problem today. Solve the following pair of linear equations. px plus qy is equal to p minus q and qx minus py is equal to p plus q. Now let us write the solution. The given equations are px plus qy is equal to p minus q and qx minus py is equal to p plus q. This is our equation 1 and this is our equation 2. Now multiplying both sides of the equation 1 by q and both sides of the equation 2 by p. Multiplying equation 1 by q and equation 2 by p, we get q multiplied by px plus q multiplied by qy is equal to q multiplied by p minus q, which implies pqx plus q square y is equal to pq minus q square. This is our equation 3. Now considering the second equation we get p multiplied by qx minus p multiplied by py is equal to p multiplied by p plus q, which implies pqx minus p square y is equal to p square plus pq. This is our equation 4. Now solving equation 3 and 4, we get pqx plus q square y is equal to pq minus q square and pqx minus p square y is equal to p square plus pq. Now subtracting this equation we get, do not forget to change the signs while subtracting. This gets cancelled. q square y plus p square y is equal to p square plus q square multiplied by y is equal to pq minus q square minus p square minus pq. Now here this gets cancelled so it implies p square plus q square multiplied by y is equal to taking minus common so we get p square plus q square. Now this and this gets cancelled so it implies y is equal to minus 1. Now substituting y is equal to minus 1 in equation 1, we get we have equation 1 as px plus qy is equal to p minus q. So which implies px plus q into minus 1 is equal to p minus q which implies px minus q is equal to p minus q. Now we see that this and this gets cancelled so it implies px is equal to p which implies x is equal to p divided by p which gets cancelled. So implies x is equal to 1 hence x is equal to 1 and y is equal to minus 1 is our required answer. I hope you understood the problem bye and have a nice day.