How many solutions does the following system of equations have #3y-6x=9, 2y-4x=6#?

1 Answer
Jan 11, 2017

We have infinite solutions.

Explanation:

The two equations are in fact identical.

If we divide the equation #3y-6x=9# on both sides by same number #3#, we get #y-2x=3#

similarly dividing #2y-4x=6# on both sides by same number #2#, we too get #y-2x=3#

Hence the two equation are identical and actually denote same line #y-2x=3# or #y=2x+3#

Hence, for any #x=x_1#, we can get #y_1=2x_1+3# and #(x_1,y_1)# is a solution to the equation and we can have infinite #(x_1,y_1)# all lying on line #y=2x+3#
graph{2x+3 [-11.54, 8.46, -4.52, 5.48]}
Hence, we have infinite solutions.