Question

How many solutions are there to the following system of equations?

4x – 14y = 6
–2x + 7y = –3

A.
1

B.
2

C.
infinitely many

D.
0

Answer 1

$4x-14y=6 \\ -2x+7y=-3 \ \ \ |\times 2 \\ \\ 4x-14y=6 \\ \underline{-4x+14y=-6} \\ 4x-4x-14y+14y=6-6 \\ 0=0 \\ always \ true \\ \\ \boxed{\hbox{infinitely many solutions}} \Leftarrow \hbox{answer C}$