SOLUTION: Which of the following systems of equations has no solution? (A) 5x + 10y = 20 4x + 8y = 16 (B) 5x + 10y = 20 x + 2y = 4 (C) 5x + 10y = 20 4x + 8y = 20 (D) None of the

Algebra ->  Linear-equations -> SOLUTION: Which of the following systems of equations has no solution? (A) 5x + 10y = 20 4x + 8y = 16 (B) 5x + 10y = 20 x + 2y = 4 (C) 5x + 10y = 20 4x + 8y = 20 (D) None of the      Log On


   

Question 205525: Which of the following systems of equations has no solution?
(A) 5x + 10y = 20 4x + 8y = 16
(B) 5x + 10y = 20 x + 2y = 4
(C) 5x + 10y = 20 4x + 8y = 20
(D) None of these
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the following systems of equations has no solution?
(A) system%285x+%2B+10y+=+20%2C+4x+%2B+8y+=+16%29

Divide the first equation through by 5, and the second
equation through by 4:

system%28x+%2B+2y+=+4%2C+x+%2B+2y+=+4%29

Those are the same line, so the system is dependent and has
infinitely many solutions.  So that's not it.

(B) system%285x+%2B+10y+=+20%2C+x+%2B+2y+=+4%29

Divide the first equation by 5:

system%28x+%2B+2y+=+4%2C+x+%2B+2y+=+4%29

Those are also the same line, so the system is dependent and has
infinitely many solutions.  So that's not it either.

(C) system%285x+%2B+10y+=+20%2C+4x+%2B+8y+=+20%29

Divide the first equation through by 5, and the second
equation through by 4:

system%28x+%2B+2y+=+4%2C+x+%2B+2y+=+5%29

The left sides are the same but the right sides are not
So they are inconsistent and have no solution.  This is
the correct choice!

Edwin