 Hello and welcome to the session. Let us discuss the following problem today. Given the linear equation 2x plus 3y minus 8 is equal to 0, write another linear equation in two variables such that geometrical representation of a pair so formed is first intersecting lines, second parallel lines and third coincident lines. Now let us write the solution. Given equation is 2x plus 3y minus 8 is equal to 0, there can be many answers possible. Here a1 is equal to 2, b1 is equal to 3 and c1 is equal to minus 8. Now for the lines to be intersecting, a1 by a2 is not equal to b1 by b2. Hence the required equation possible is 3x plus 2y minus 6 is equal to 0, where a2 is equal to 3, b2 is equal to 2 and c2 is equal to minus 6. And now a1 by a2 is equal to 2 by 3, b1 by b2 is equal to 3 by 2 and c1 by c2 is equal to minus 8 by minus 6 which is equal to 4 by 3. Therefore we find here a1 by a2 is not equal to b1 by b2. Hence one possible answer is 3x plus 2y minus 6 is equal to 0. Therefore this equation we have got for the lines to be intersecting. Now for the lines to be parallel, we have a1 by a2 is equal to b1 by b2 is not equal to c1 by c2. So one possible answer is 2x plus 3y minus 6 is equal to 0, where a2 is equal to 2, b2 is equal to 3 and c2 is equal to minus 6. Now a1 by a2 is equal to 2 by 2 which is equal to 1, b1 by b2 is equal to 3 by 3 which is equal to 1 and c1 by c2 is equal to minus 8 by minus 6 which is equal to 4 by 3. Therefore we find that a1 by a2 is equal to b1 by b2 is not equal to c1 by c2. Hence one possible answer is 2x plus 3y minus 6 is equal to 0. Therefore this is the equation for lines to be parallel. Now for the lines to be coincident a1 by a2 is equal to b1 by b2 is equal to c1 by c2. Therefore one possible answer is 6x plus 9 by minus 24 is equal to 0, where a2 is equal to 6, b2 is equal to 9 and c2 is equal to minus 24. Now a1 by a2 is equal to 2 by 6 which is equal to 1 by 3 and b1 by b2 is equal to 3 by 9 which is equal to 1 by 3 and c1 by c2 is equal to minus 8 by minus 24 which is equal to 1 by 3. So we find that a1 by a2 is equal to b1 by b2 is equal to c1 by c2. Hence one possible answer is 6x plus 9y minus 24 is equal to 0. Therefore this is the equation for lines to be coincident. I hope you understood this problem. Bye and have a nice day.