Decide whether the given ordered pair is a solution of the given system. \[ \begin{array}{c} (5,-7) \\ x+y=-2 \\ 2 x+3 y=16 \end{array} \] Is the s:dered pair a solution to the system of equations?

Step 1 ：Substitute the values of the ordered pair into the system of equations.

Step 2 ：For the first equation, substitute x=5 and y=-7, we get 5+(-7)=-2 which is true.

Step 3 ：For the second equation, substitute x=5 and y=-7, we get 2*5+3*(-7)=16 which is false.

Step 4 ：Since not all equations are true, the ordered pair (5,-7) is not a solution to the system of equations.

Step 5 ：\(\boxed{\text{The ordered pair (5,-7) is not a solution to the system of equations.}}\)