 Hi, my name is Shashi and I am going to help you to solve the following question. Question is, on comparing the ratios A1 upon A2, B1 upon B2 and C1 upon C2, find out whether the following pair of linear equations are consistent or inconsistent. Equations are 3 upon 2x plus 5 upon 3y is equal to 7. Other equation is 9x minus 10y is equal to 14. 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. Let us start with the solution now. Rewriting the given equations, we get 3 upon 2x plus 5 upon 3y minus 7 is equal to 0 and 9x minus 10y minus 14 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. Here we can see A1 is equal to 3 upon 2, B1 is equal to 5 upon 3, C1 is equal to minus 7, A2 is equal to 9, B2 is equal to minus 10 and C2 is equal to minus 14. Now A1 upon A2 is equal to 3 upon 2 multiplied by 9 which is equal to 1 upon 6. Now we will calculate B1 upon B2 which is equal to 5 upon 3 multiplied by minus 10 which is equal to minus 1 upon 6. Now we will calculate C1 upon C2 which is equal to minus 7 upon minus 14 equal to 1 upon 2. Now we can see A1 upon A2 is not equal to B1 upon B2. So the given system of equation is consistent. By the K idea we know that if A1 upon A2 is not equal to B1 upon B2 then given system of equations is consistent. So the given pair of equations is consistent. This is our final answer. This completes the session. Hope you understood the session well. Good bye and take care.