 Hello and welcome to the session. Let us discuss the following question today. Is the following pair of linear equations has unique solutions, no solutions or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. And we have x-3y-7 is equal to 0 and 3x-3y-15 is equal to 0. Now let us write the solution. Given equations are 3y-7 is equal to 0 and 3x-3y-15 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. So we have a1 is equal to 1, a2 is equal to 3, b1 is equal to minus 3, b2 is equal to minus 3, c1 is equal to minus 7 and c2 is equal to minus 15. Now a1 by a2 is equal to 1 by 3, b1 by b2 is equal to minus 3 by minus 3 which is equal to 1 and c1 by c2 is equal to minus 7 by minus 15 which is equal to 7 by 15. Which implies a1 by a2 is not equal to b1 by b2 as 1 by 3 is not equal to 1. So it implies a unique solution. So now solving by cross multiplication method. So we have x divided by b1c2 minus b2c1 which is equal to y by c1 a2 minus c2 a1 which is equal to 1 by a1b2 minus b1a2. Now which implies x upon substituting the values of a1b2 b1c1 a2b2c2. So we get x upon minus 3 minus 15 minus minus 3 multiplied by minus 7 which is equal to y by minus 1 multiplied by plus 3 minus minus 15 multiplied by 1 which is equal to 1 upon 1 multiplied by minus 3 minus 3 multiplied by minus 3. Which implies x upon 45 minus 21 is equal to y upon minus 21 plus 15 which is equal to 1 upon minus 3 plus 9. Which implies x upon 24 is equal to y by minus 6 is equal to 1 by 6. Now x by 24 is equal to 1 by 6 which implies 6x is equal to 24 which implies x is equal to 24 by 6. This gets cancelled by 4 so it implies x is equal to 4. Now similarly y by minus 6 is equal to 1 by 6 which implies 6y is equal to minus 6 which implies y is equal to minus 6 by 6. This one gets cancelled so which implies y is equal to minus 1. Now hence the given system of equations has unique solution with x is equal to 4 and y is equal to minus 1. And this is our required answer. I hope you understood the equation. Bye and have a nice day.