 Hi and welcome to the session. My name is Reshi and I am going to help you to solve the following question. Question is, on comparing the ratios even upon A2, B1 upon B2 and C1 upon C2, find out whether the following pair of linear equations are consistent or inconsistent. Equations are 2x minus 3y is equal to 8 and 4x minus 6y is equal to 9. 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. This is the key idea to solve the given question. Let us start with the solution now. We can rewrite the given equations as 2x minus 3y minus 8 is equal to 0 and 4x minus 6y is equal to 0. Now, we can compare the two equations with A1x plus B1y plus C1 is equal to 0 and A2x plus B2y is equal to 0. Now, we can compare the two equations with A1x plus B1y plus C1 is equal to 0 and A2x plus B2y is equal to 0. A1x plus B1y plus C1 is equal to 0 and A2x plus B2y plus C2 is equal to 0. Here, we can see that the values of A1 is equal to 2, B1 is equal to minus 3, C1 is equal to minus 8. A1 is equal to 2, B1 is equal to minus 3, C1 is equal to minus 8. Then, A2 is equal to 4, B2 is equal to minus 6, C2 is equal to minus 9. Now, A1 upon A2 is equal to 2 upon 4 which is equal to 1 upon 2, B1 upon B2 is equal to minus 3 upon minus 6, minus and minus get cancelled and our answer is 1 upon 2. C1 upon C2 is equal to minus 8 upon minus 9 which is equal to 8 upon 9. Thus, we get A1 upon A2 is equal to B1 upon B2 is not equal to C1 upon C2. Now, by key idea we know if A1 upon A2 is equal to B1 upon B2 is not equal to C1 upon C2 then given system of equations is inconsistent. So, the given system of equations is inconsistent. This is our final answer. This completes the session. Hope you understood the session. Goodbye and take care.