 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question is, on comparing the ratios A1 upon A2, B1 upon B2, C1 upon C2, find out whether the lines representing the following pairs of linear equations intersect at a point are parallel or coincident. The equations are 9x plus 3y plus 12 is equal to 0 and the other equation is 18x plus 6y plus 24 is equal to 0. First of all, let us understand that if in a pair of linear equations A1x plus B1y plus C is equal to 0 and A2x plus B2y plus C2 is equal to 0, we have A1 upon A2 is not equal to B1 upon B2 then the lines intersect each other. If A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2 then the lines are coincident and if A1 upon A2 is equal to B1 upon B2 is not equal to C1 upon C2 then the lines are parallel. This is the key idea to solve the given question. Let us now start with the solution. Let us rewrite the equations given in the question. That is 9x plus 3y plus 12 is equal to 0 and 18x plus 6y plus 24 is equal to 0. These equations are of the form A1x plus B1y plus C1 is equal to 0 and A2x plus B2y plus C2 is equal to 0. Comparing the equations we get A1 is equal to 9, B1 is equal to 3 and C1 is equal to 12. Similarly comparing the other two equations we get A2 is equal to 18, B2 is equal to 6 and C2 is equal to 24. Now A1 upon A2 is equal to 9 upon 18 which is further equal to 1 upon 2. Similarly B1 upon B2 is equal to 3 upon 6 which is equal to 1 upon 2. Now C1 upon C2 is equal to 12 upon 24 is equal to 1 upon 2. Now we can see that A1 upon A2 is equal to 1 upon 2. B1 upon B2 is equal to 1 upon 2 and C1 upon C2 is equal to 1 upon 2 which implies A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2 equal to 1 upon 2. Right? By the key idea the lines representing the equations 9x plus 3y plus 12 is equal to 0 and 18x plus 6y plus 24 is equal to 0 are coincident. Hence the lines are coincident is our required answer. Hence this completes the session. Hope you understood the session. Take care and good bye.