 Hello and welcome to the session. Let us understand the following problem today. Solve the following pair of equations by reducing them to a pair of linear equation given to us 2 by root x plus 3 by root y is equal to 2 and 4 by root x minus 9 by root y is equal to minus 1. Now let us write the solution. The given pair of equation can be written as 1 by root y is equal to 2 root y is equal to minus 1. Now it is equal to p 1 by root y is equal to q. So we get q is equal to 2 p minus 9 q is equal to minus 1. Let us name these equations as 1 and 2. Now between equations 1 and 2 we get first of all multiplying equation 1 by 3 we get plus 9 q is equal to 6. I think the second equation as it is we get 4 p minus 9 q is equal to minus 1. Now adding these two equations we get this gets cancels 6 p plus 4 p gives us 9 p is equal to 6 minus 1 gives us 5. Therefore p is equal to 5 by 10 and p is equal to 1 by 2. Let us name these equations as 3 and 4. Now trituting is equal to half in equation 3 we get putting p is equal to half in this equation we get half plus 9 q is equal to 6. Now solving this this gets cancels. So we get 3 plus 9 q is equal to 6 which implies 9 q is equal to 6 minus 3 which implies 9 q is equal to 3 which implies q is equal to 1 by 3 is equal to 1 by 2 and q is equal to 1 by 3. Now we have assumed earlier 1 by root x is equal to p and 1 by root y is equal to q. So 1 by root x is equal to p and 1 by root y is equal to q which implies 1 by root x is equal to 1 by 2 and this implies 1 by root y is equal to 1 by 3. Sharing both sides x is equal to 1 by 4 which implies x is the problem bye and have a nice day.