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!

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,