Given the system of equations:
[tex]\begin{gathered} y=-x+3 \\ y=-x+5 \end{gathered}[/tex]
Since the left hand side of both equatiions are same, equate the right hand side.
[tex]-x+3=-x+5[/tex]
Add x on both sides of the equation.
[tex]\begin{gathered} -x+3+x=-x+5+x \\ 3=5 \end{gathered}[/tex]
which is not possible. Hence the given system of equations is inconsistent.
