 Hello and welcome to the session. In this session, we will discuss a question which says that U is grammar's rule to solve for U and V. 5 over U plus 6 over V is equal to 11 and 10 over U plus 9 over V is equal to 21. Now before starting the solution of this question, we should know a result. And that is the grammar's rule. For the equations A1x plus B1y is equal to C1 and A2x plus B2y is equal to C2, the solution equations in determinant form is given as equal to the determinant with the elements in first row as C1, B1 and the elements in the second row as C2, B2 over the determinant with the elements in first row as A1, B1 and the elements in the second row as A2, B2 which is equal to the determinant dx in the numerator and the determinant d in the denominator. Now the determinant d in the denominator is really the determinant of the coefficients in these equations. In the determinant dx, the coefficients of x that is A1, A2 are still terms C1, C2 and y is equal to the determinant with the elements in first row as A1, C1 and the elements in second row as and the elements in the second row as the determinant dy over the determinant dy. The coefficient of y replaced by the constant terms C1 and C1 is not equal to 0. This is how we can find the solution of the given equations by using the grammar rule. Now this result will work out as a key idea for solving that this question. And now we will start with the solution. Now given these two equations and we have to solve them for u and v using grammar's rule. So given x over v is equal to 11 and 10 over u plus 9 over v is equal to 21. Now putting 1 over v is equal to 1 over v is equal to b, the equation number 1 is equal to 11, b is equal to 21. Now by using the result which is given in the key idea as A1 as b1, 9 as b2, 11 as b will be equal to the determinant in first row as A1 b1 that will be 5, that will be 10, 9 is equal to 9 into 5 minus 10 into 6. That will be 5 which is equal to minus 15. Therefore d is not equal to 0. Therefore the solution of the given equations exists. The determinant dA which is equal to the determinant with the elements in the first row as... Now using the values from these equations we will determinant with the elements in the first row as 11, 6. And the element on solving this is equal to 99 minus 126 that is 9 into 11 which is 99 minus 21 into 6 that is 126 which is equal to minus 27. Now let us find the determinant db which is equal to the determinant with the elements in the first row as and the elements in the second row as A2 6 from these equations. Determinant, so this is equal to m which is 105 minus 7 that is 110 which is equal to minus 5. Now the determinant dA over the determinant d which will be equal to... Now the determinant dA is equal to minus 27 and the determinant d is minus 5 is equal to minus 27 over minus 15 9 over 5. Now v is equal to the determinant db over determinant d which is equal to... Now the determinant db is equal to minus 5 so this is equal to 1 by 3 and 1 by v as b. Now it implies 1 by v is equal to b implies 1 by v is equal to... Now b is 1 by 3 so this is equal to 1 by 3 which further implies v is equal to 12 the given question and that is all for this session. Hope you all have enjoyed the session.