 Hi, and welcome to the session. I am Deepika here. Let's discuss the question. Examine the consistency of the system of equations 2x-y is equal to 5, x plus y is equal to 4. Let us first understand what is the meaning of consistent system. A system of equations is said to be consistent if its solution one or more exists. Inconsistent system? A system of equations is said to be inconsistent if its solution does not exist. Let's start the solution. The given system of equations is x minus y is equal to 5 and x plus y is equal to 4. The system of equations can be written in the form A x is equal to B where A is equal to 2 minus 1, 1, 1, x is equal to x, y and B is equal to 5, 4. Now determinant of A is equal to 2 minus minus of 1 which is equal to 2 plus 1 that is equal to 3 which is non-zero. Hence A is a non-singular lattice and so has a unique solution. Therefore, the given system of equations is consistent. Hence the answer for the above system of equations is consistent. I hope the question is clear to you. Bye and have a good day.