The first row of the matrix tells us that

	x = -y + 5.

So far, so good. However, if we represent the second row of the matrix as an equation, we get

	0x + 0y = 3

that is,

	0 = 3.

Thus, the assumption that there is a solution of the system of equations leads to an absurd conclusion. Therefore, there is no solution of the system.

See Section 2.1, Example 4, in Finite Mathematics Applied to the Real World or Finite Mathematics and Calculus Applied to the Real World. for additional discussion of this point.