 Hello friends, welcome to the session. I am Mankap. We are going to discuss pair of linear equations in two variables. We have to form the pair of linear equations in the following problems and find the solutions if they exist by the elimination method. A given problem is, 5 years ago, Noory was twice as old as Sonu. 10 years later, Noory will be twice as old as Sonu. How old are Noory and Sonu? So, let's have the solution. So, let the present age of Noory be x years and let the present age of Sonu be y years. 5 years ago, Noory was present age minus 5 years. 5 years ago, Sonu was present age of Sonu minus 5 years. According to question, we are given that 5 years ago, Noory was twice as old as Sonu. So, according to question, Noory that is x minus 5 was twice as old as Sonu which is y minus 5. This implies x minus 5 equal to 3 y minus 15. This implies x minus 3 y plus 10 equal to 0. So, this is our first equation. Now, we see that 10 years later, Noory will be present age plus 10 years. 10 years later, Sonu will be present age of Sonu plus 10 years. Now, again from the question, we see that Noory will be twice as old as Sonu. So, this is Noory that is x plus 10 will be twice as old as Sonu which is y plus 10. This implies x plus 10 equal to 2 y plus 20. This implies x minus 2 y minus 10 equal to 0. So, this is our second equation. Hence, the equations are x minus 3 y plus 10 equal to 0 and second equation is x minus 2 y minus 10 equal to 0. This is our second equation. Now, on subtracting equation second from we get minus x minus 3 y minus of minus 2 y plus 10 minus of minus 10 equal to 0. This implies x minus x is 0 minus 3 y plus 2 y plus 10 plus 10 equal to 0. This implies minus y plus 20 equal to 0. This implies y equal to 20. Now, substituting value of y in equation first, we get our first equation is x minus 3 y plus 10 equal to 0. Now, here we will substitute y equal to 20. This gives us x minus 3 into 20 plus 10 equal to 0. This implies x minus 60 plus 10 equal to 0. This implies x minus 50 equal to 0. This implies x equal to 50. Hence, the equations are x minus 3 y plus 10 equal to 0 and the second equation is x minus 2 y minus 10 equal to 0. Where x and y are Nourie's, Sonu's, Ages respectively, Nourie which is x, Nourie's Ages 50 years and Sonu's Age which is represented by y is 20 years. Hope you understood the solution and enjoyed the session. Goodbye and take care.