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.

If i'm correct the answer is $15.97

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.