 Hello and welcome to the session. I am Deepika here. Let's discuss the question. Question says, examining the consistency of the system of equations, x plus 3y is equal to 5, 2x plus 6y is equal to 8. We know that a system of equations is said to be consistent if its solution exists. And it is said to be inconsistent if its solution does not exist. So let's start the solution. The given system of equations is 3y is equal to 5 and 2x plus 6y is equal to 8. The above system of equations can be written in the form is equal to b where x is equal to 1 is equal to xy and b is equal to 5, 8. Now determinant of a equal to x minus 6 is equal to 0. This implies these are singular matrix. In case we will calculate adjoint a into b because r determinant is equal to 0. We know that for a square matrix of order 2 the adjoint a can also be obtained by interchanging a11 and a22 and by changing signs of a12 and a21. That is therefore our adjoint a is equal to minus 3 minus 2. Therefore adjoint a into b is equal to x minus 2 minus 3 1 into b 5, 8. This is equal to minus 24 and minus 10 plus 8 is equal to minus 6 minus 2 is not equal to 0 matrix. For adjoint a into b is not equal to 0 this implies the given system of equations is inconsistent. The answer for above system of equations is they are inconsistent. I hope the question is clear to you. Bye and have a nice day.