How many solutions does this system have? 2 x - 3 y = 10. -4 x + 6 y = - 20. A) One
B) Two
C) An infinite number
D) No solution

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

Step-by-step explanation:

We are given the following system of equations:

   2x − 3y = 10 ;

     -4x + 6y  =  -20 ;

  Let us take the second equation:

   -4x + 6y  =  -20 ;

     and multiply each side by "-1 " ; to get rid of the "negative numbers" ; and to rewrite the equation without the "negative numbers" :    

       - 1 * { - 4x + 6y }  =  -1 * (-20} ;

  to get:

       4x − 6y = -20 ;

Now, let us simply this equation further; by divide each side of the equation by "2" ;

       (4x − 6y) / 2  =  (-20) / 2 ;

          → [ (4x) / 2 ]    −  [ (6y) / 2 ]  =  -10 ;

   to get:   2x  −  3y  = -10 ;

Then we have: 2x − 3y = 10 ;  

                    Note:    10 ≠ -10 .

So the answer is: [D]: " No solution."

Hope this explanation helps you!  Best wishes!

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