 Hello friends, welcome to the session on Malka. 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. Our problem is if we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1 by 2 if we only add 1 to the denominator. What is the fraction? So let's start with the solution. Now, let the numerator be x and let the denominator be y. Therefore, fraction is equal to x upon y. Now, from the question we see that if we add 1 to the numerator, that is x plus 1 and subtract 1 from the denominator that is y minus 1, then our fraction is equal to 1. So this implies on cross multiplying we get x plus 1 equal to y minus 1. This implies x minus y plus 1 plus 1 equal to 0. This implies x minus y plus 2 equal to 0. So this is our first equation. Now, again from the question we see that if we only add 1 to the denominator, then our fraction is 1 by 2. So this can be written as x upon y plus 1 equal to 1 by 2. Now on cross multiplying we get 2x equal to 1 into y plus 1. This implies 2x minus y minus 1 equal to 0. So this is our second equation. Hence, the equations are x minus y plus 2 equal to 0 and 2x minus y minus 1 equal to 0. Now, subtracting equation second from first minus 2x minus y minus of minus y plus 2 minus of minus 1 equal to 0. This implies minus x minus y plus y plus 2 plus 1 equal to 0. This implies minus x plus 3 equal to 0. This implies x equal to 3. Now, on substituting x equal to 3 in equation first, we get our equation first is x minus y plus 2 equal to 0 and on place of x we write 3. This will give us 3 minus y plus 2 equal to 0. This implies y minus y plus 5 equal to 0. This implies y equal to 5. Therefore, the fraction is upon y which is equal to 3 upon 5. Hence the equations are x minus y plus 2 equal to 0 and 2x minus y minus 1 equal to 0 where x and y are the numerator and denominator and the fraction is equal to 3 upon 5. Hope you understood the solution and enjoyed the session. Goodbye and take care.