Aset of equations is given below:
equation c: y = 4x + 8
equation d: y = 4x + 2
which of the following best describes the solution to the given set of equations?
no solution
one solution
two solutions
infinitely many solutions

The answer is:  [A]:  "No solution" .

Note:  Given:

  y = 4x + 8 ;
  y = 4x + 2 ;


Since:  "y = y" ;

4x + 8 = 4x + 2 ; which is not true;

 4x  +  8  ≠  4x  +  2 ;  since,  "8  ≠ 2" ;

Note:  Suppose:  "4x + 8 = 4x + 2" ; 

→ Subtract "4x" from each side of the equation:

4x + 8 − 4x  = 4x + 2 − 4x ;

to get:

 " 8 = 2 " ;  not true ; since  "8 ≠ 2" ;

Also, suppose:

 4x + 8 = 4x + 2 ;

→ Subtract "2" from BOTH SIDES of the equation;

4x + 8 − 2 = 4x + 2 − 2 ;

to get:

4x + 6 = 4x

(Note:  "4x + 0 = 4x" ;  but "4x + 6 ≠ 4x") l

But even if we have:

4x + 6 = 4x ;

→ Subtract "4x" from EACH side of the equation:

4x + 6 − 4x  = 4x − 4x ;

to get:

   6 = 0 ; which is not true;  "6 ≠ 0" . 

The correct answer is:  [A]:  "No solution" .