 Hi, and welcome to the session I am going to pick up here. Let's discuss the question. Examining the consistency of the system of equations, 5x minus y plus 4z is equal to 5, 2x plus 3y plus 5z is equal to 2, 5x minus 2y plus 6z is equal to minus 1. Let's start the solution. The given system of equations can be written in the form x is equal to b where x is equal to 5 minus 1, 4, 2, 3, 5, 5, minus 2, 6 is equal to x, y, z and b is equal to 5, 2, minus 1. We know that a system of equations is said to be consistent if its solution exists and a system of equations is said to be inconsistent if its solution does not exist. So, we will first find out determinant of a. Now, determinant of a is equal to 5 into 18 plus 10 minus minus 1 into 12 minus 25 plus 4 into minus 4 minus 15. This is equal to 5 into 28 plus 1 into minus 13 plus 4 into minus 19. This is equal to 140 minus 13 minus 76. Which is equal to 140 minus 140 minus 89 that is equal to 51. This implies determinant of a is not equal to 0 because determinant of a comes out to be 51 which is not equal to 0. So, a is non-singular matrix so has a unique solution. This implies the given system of equations is consistent. So, the answer for the above system of equations is that they are consistent. I hope the question is clear to you. Bye and have a good day.