 Hi and welcome to the session. I am Deepika here. Let's discuss the question. Examining the consistency of the system of equations, x plus 2y is equal to 2, 2x plus 3y is equal to 3. Before examining the consistency of the system of equations, let us understand what is the meaning of consistent system. A system of equation is said to be consistent if its solution one or more exists. A system of equation is said to be inconsistent if its solution does not exist. Now, start the solution. The given system of equations are x plus 2y is equal to 2 and 2x plus 3y is equal to 3. The above system of equations can be written in the form x is equal to b where a is equal to 1, 2, 2, 3, x is equal to xy and b is equal to 2, 2, 3. Now, determinant of a is equal to 3 minus 4 which is equal to minus 1 that is not equal to 0. Hence, a is a non-singular matrix and so has a unique solution. This implies the given system of equation is consistent. Hence, our answer for the above system of equations is they are consistent. I hope question is clear to you. Bye and have a nice day.