Which of the following ordered pairs is a solution of the given system of linear equations? ( give a good explanation for brainliest and full ratings. )

The answer is:  [D]:  " (-3, 5) " .

We are given the following two equations:

    x + y = 2 ;

   y = -2x - 1 ;


Let us rewrite the first equation:

  x + y = 2 ;  solve in terms of "y" ;

Subtract "x" from EACH SIDE of the equation; to isolate "y" on one side of the equation ; and to solve in terms of "y" ;

 x + y - x = 2 - x  ;

    y = 2 - x  ;

Now, let us rewrite this equation, and the second equation:

  y = 2 - x  ;

y = - 2x - 1

Start with "Choice [A]:  (5, -3) " ;  When x = 5, y = 3.  Do these values hold true for BOTH of the two (2) equations? 
     Start with:  " y = 2 - x " ;   "-3 =?  2 - 5 ? "  ;  "-3 =? -7 ? "  No!  So we can rule out "Choice [A]" without even considering the second equation.

Then, consider:  "Choice [B]:  (-1, 3) " ;  When x = -1, y = 3.  Do these values hold true for BOTH of the two (2) equations? 
     Start with " y = 2 - x " .  "3 =? 2- (-1) ? " ;   "3 =? 2 + 1 ?  Yes!
     Now, let us try plugging these values; "x = -1" and "y = 3" into the second equation:

       " y = - 2x - 1 " ;   "3 =? -2(-1) - 1 ? " ;  "3 =? 2 - 1 ? " ;  "3 =? 1 ? No! 
So we can rule out "Choice [B]"

Then, consider:  "Choice [C]:  (3, -1) " ;  When x = 3, y = -1.  Do these values hold true for BOTH of the two (2) equations? 
     Start with " y = 2 - x " .  "-1 =? 2 - (3) ? " ;  "-1 =? -1 ?  Yes!
     Now, let us try plugging these values; "x = 3" and "y = -1" into the second equation:

       " y = - 2x - 1 " ;   "-1 =? -2(3) - 1 ? " ;  "-1 =? -6 - 1 ? " ;  "-1 =? -7 ? No! 
So we can rule out "Choice [C]" .

This leaves us with:  "Choice [D]".  But let us try working out this answer choice.

     Consider  "Choice [D]:  (-3, 5) " ;  When x = -3, y = 5.  Do these values hold true for BOTH of the two (2) equations? 
   Start with " y = 2 - x " .  "5 =? 2 - (-3) ? " ;  "5 =? 2 + 3 ? " ;  "5 =? 5 ?" ; Yes!
     Now, let us try plugging these values; "x = 3" and "y = -1" into the second equation:

     " y = - 2x - 1 " ;   "5 =? -2(-3) - 1 ? " ;  "5 =? 6 - 1 ? " ;  "5 =? 5" ? ;  Yes! 

So, Answer choice:  [D]:  " (-3, 5) " — is the correct answer.