 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question is form the pair of linear equations for the following problems and find their solution by substitution method. Fifth part is a fraction becomes 9 upon 11 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes 5 upon 6. Find the fraction. Let us start with the solution now. In the question the numerator and the denominator both are unknown. So let us assume the numerator equal to x and the denominator is equal to what? First condition in the question is the fraction becomes 9 upon 11 if 2 is added to both the numerator and the denominator. y plus 2 must be equal to 9 upon 11. This implies y, y plus 2. We get this equation which further implies 22 is equal to 9 where the condition given in the question is that if 3 both the numerator and the denominator it becomes 5 upon 6 multiplied by. Let us name this equation as equations are 11x minus 9y plus 4 is equal to 0 minus 5y plus 3 is equal to 0. From equation 1 we get upon 11. Let us name this equation as we will substitute the value of n equation. Now substituting the value of x in equation 2 we get 6 multiplied by 9y minus 4 upon 11 minus 5y plus 3 is equal to 0. Multiplying the equation by 11 on both sides we get 54y minus 24 minus 55y is equal to 0. 33 plus 24 is equal to minus 9. We can say y is equal to now we will substitute this value of y in the equation 3 to get the value of x. Now substituting the value of y in equation 3 we get x is equal to multiplied by 9 minus 4 upon 11. This implies 81 minus 4 upon 11, 77 upon 11 or we can say x is equal to y is equal to 9. So our required fraction is 7 upon 9. Our required equations are 11x minus 9y plus 4 is equal to 0, y plus 3 is equal to 0, 7 and y is equal to 9 is the solution of the given equations where x is the numerator and y is the denominator and the required fraction is equal to 7 upon 9. This is our final answer. This completes the session. Hope you understood the session.