 Hello and welcome to the session. Let us understand the following question today. For which values of a and b does the following pair of linear equations have an infinite number of solutions? We have 2x plus 3y is equal to 7 and a minus bx plus a plus by is equal to 3a plus b minus 2. Now let us write the solution. Given equations are 2x plus 3y minus 7 is equal to 0 and a minus bx plus a plus by minus 3a minus b plus 2 is equal to 0. Now comparing the equations with a1x plus b1y plus c1 is equal to 0 and a2x plus b2y plus c2 is equal to 0. We get a1 is equal to 2, a2 is equal to a minus b, b1 is equal to 3, b2 is equal to a plus b, c1 is equal to minus 7, c2 is equal to minus 3a minus b plus 2. Now a1 by a2 is equal to 2 by a minus b, b1 by b2 is equal to 3 by a plus b and c1 by c2 is equal to minus 7 by minus 3a minus b plus 2. Now the given system of equations infinitely many solutions if a1 by a2 is equal to b1 by b2 is equal to c1 by c2. So therefore 2 by a minus b is equal to 3 by a plus b is equal to minus 7 by minus 3a minus b plus 2. Now first answering these two terms so we get 2 by a minus b is equal to 3 by a plus b. Now on cross multiplication it implies 2a plus 2b is equal to 3a minus 3b this implies 2a minus 3a plus 2b plus 3b is equal to 0. Which implies minus a plus 5b is equal to 0. Let us name this equation as number 1. Now consider these two so we get 3 by a plus b is equal to minus 7 by minus 3a minus b plus 2. Again cross multiply so it implies 3 multiplied by minus 3a minus b plus 2 is equal to minus 7 multiplied by a plus b. Which implies opening the brackets we get minus 9a minus 3b plus 6 is equal to minus 7a minus 7b. Which implies minus 9a plus 7a minus 3b plus 7b plus 6 is equal to 0. Which implies minus 2a plus 4b plus 6 is equal to 0. Now taking two common so we get it implies minus a plus 2b is equal to minus 3. Better name this is equation number 2. So we have got two equation as minus a plus 5b is equal to 0 and minus a plus 2b is equal to minus 3. Now subtracting these two equations we get do not forget to change the sign while subtracting. This gets cancelled so we get 5b minus 2b is equal to 3b which is equal to plus 3. Which implies b is equal to 1. Now substituting b is equal to 1 in equation 1 we get minus a plus 5 into 1 is equal to 0. Which implies minus a plus 5 is equal to 0. Which implies minus a is equal to minus 5. This minus and minus gets cancelled so we are left with a is equal to 5. Hence a is equal to 5 and b is equal to 1 is our required answer. I hope you understood the question. Bye and have a nice day.