 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, P1 upon P2 and C1 upon C2, find out whether the following pair of linear equations are consistent or inconsistent. The given equations are 4 upon 3x plus 2y is equal to 8 and 2x plus 3y is equal to 12. First of all let us understand that the system of equations A1x plus B1y plus C1 is equal to 0 and A2x plus B2y plus C2 is equal to 0 is consistent if A1 upon A2 is not equal to B1 upon B2. The system of equations is consistent if A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2. The system of equations is inconsistent if A1 upon A2 is equal to B1 upon B2 is not equal to C1 upon C2. This is the key idea to solve the given question. Let us now start with the solution. We can rewrite the given equations as 4 upon 3x plus 2y minus 8 is equal to 0 and 2x plus 3y minus 12 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 can see A1 is equal to 4 upon 3, B1 is equal to 2, C1 is equal to minus 8, A2 is equal to 2, B2 is equal to 3 and C2 is equal to minus 12. Now A1 upon A2 is equal to 4 upon 3 multiplied by 2 which is equal to 2 upon 3, B1 upon B2 is equal to 2 upon 3, C1 upon C2 is equal to minus 8 upon minus 12 which is equal to 2 upon 3. So we get A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2 is equal to 2 upon 3, right? By key idea we know that if A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2 then the given pair of linear equations is consistent. Hence the given pair of equations is consistent is the required answer. This completes the session. Hope you understood the session. Take care and goodbye.