 Hello and welcome to this session. Let us understand the following question today. Is the following pair of linear equation has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. We have 2x plus y is equal to 5 and 3x plus 2y is equal to 8. Now before starting with the solution, let us understand what is the unique solution, no solution, and infinitely many solutions. If the lines are represented by the equation a1x plus b1y plus c1 is equal to 0 and a2x plus b2y plus a2 is equal to 0, then if a1 by a2 is not equal to b1 by b2, it implies unique solution. If a1 by a2 is equal to b1 by b2 is equal to c1 by c2, then it implies infinitely many solutions. If a1 by a2 is equal to b1 by b2 is not equal to c1 by c2, it implies no solution. Now this is the key idea to our question. Now, let us write the solution. The given equations are 2x plus y is equal to 5 or it can be written as 2x plus y minus 5 is equal to 0 and 3x plus 2y is equal to 8 or it can be written as 3x plus 2y minus 8 is equal to 0. This is our equation 1 and this is our equation 2. Now comparing the equations with a1x plus b1y plus c1 is equal to 0 and a2x plus b2y plus c2 is equal to 0, then we have a1 is equal to 2, a2 is equal to 3, b1 is equal to 1, b2 is equal to 2, c1 is equal to minus 5, c2 is equal to minus 8. Now a1 by a2 is equal to 2 by 3, b1 by b2 is equal to 1 by 2 and c1 by c2 is equal to minus 5 by minus 8 which is equal to 5 by 8. So we can see that a1 by a2 is not equal to b1 by b2. Now let us see our key idea. Now if a1 by a2 is not equal to b1 by b2 then we have unique solution. So for unique solution we have to find it by using cross multiplication method. It implies unique solution. Now solving by cross multiplication method. Now it says x by b1 c2 minus b2 c1 is equal to y divided by c1 a2 minus c2 a1 is equal to 1 divided by a1 b2 minus a2 b1 which implies x upon 1 into minus 8 minus 2 into minus 5 is equal to y upon minus 5 into 3 minus minus 8 into 2 is equal to 1 upon 2 into 2 minus 3 into 1. Now which implies x upon minus 8 plus 10 which is equal to y upon minus 15 plus 16 equal to 1 upon 4 minus 3 which implies x upon 2 equal to y upon 1 is equal to 1 upon 1. Now it implies x by 2 is equal to 1 which implies x is equal to 2. Now similarly implies y upon 1 is equal to 1 which implies y is equal to 1. Hence the given system of equations has unique solution with x is equal to 2 and y is equal to 1. It is our required answer. I hope you understood the question. Bye and have a nice day.