 Hi and welcome to the session. I am Priyanka and I will be helping you with exercise 1.2 question number 23 on page 14. The question says find the solution such that u is not equal to 0, v is not equal to 0 of the following. The equation says 2u plus v is equal to 11 by 3u v and u plus 3v is equal to 11 by 3u v. So let us start with our solution first. Now as we can see let us name this as the first equation and this as the second equation which is given to us. Now as we can see that we are having variables on the right hand side also. So first of all we will be multiplying both the sides of the first equation as well as second equation by uv so as to simplify our equation. On doing it we have 2u that is not multiplying but dividing so that we can get rid of the uv which is given in the RHS. So on doing it we have 2u divided by uv plus v divided by uv is equal to 7 by 3u v divided by uv. Similarly u divided by uv plus 3v divided by uv is equal to 11u v divided by 3u v right. Now these u the v's they will get cancelled out and we are left with 2 divided by u plus sorry v plus 1 divided by u is equal to 7 by 3 and 1 divided by v plus 3 divided by u is equal to 11 by 3. Now to make it more simpler let us multiply multiply both sides of these equation by 3 and let us say that 1 by v is equal to x and 1 by u is equal to y. So now we will be having 6x plus 3y is equal to 7 and 3x plus 9y is equal to 11 got it. Let us say this as a third equation and this as a fourth equation. Now we will be solving these equation by equating the coefficient of x and for doing it we need to multiply fourth equation by 2 and on doing it we have 6x plus 3y is equal to 7 and 6x plus 18y is equal to 22. Now on subtracting from 5 we have again from 6x we will subtract 6x from 3y we will subtract 18y and from 7 we will subtract 22. These two will get cancelled out and we are left with minus 15y equal to minus 15 that is the value of y as 1. Now on substituting the value of y from 7 in let us say 6 we have 6x plus 18 multiplied by 1 is equal to 22. 6x is equal to 22 minus 18 the value of x as 4 by 6 or we can also write it as 2 by 3. So the value of x is coming to be 2 by 3. Now remember we need to find the value of u and v not x and y. So we have assumed that 1 by v is equal to x and 1 by u is equal to y right. So we have 1 by v is equal to 2 by 3 and 1 by u as 1. So we can easily say that the value of v is 3 by 2 and the value of u is equal to 1. So this completes the 23rd question of exercise 1.2 hope you enjoyed this session do take care of all your calculation remember to find out the value of u and v don't leave the question by finding out the value of x and y and best of luck.