How do you solve the system by graphing #3x – 6y = 12# and #9x + 2y = –24#?

1 Answer
Aug 23, 2017

Answer:

#x = -2 and y =-3#

Explanation:

There is no single variable, so substitution is not a good method in this case. However, notice that the signs of the #y#terms are opposite. It will be easy to make the #y#-terms into additive inverses.

#color(white)(xxxxxxx)9x+2y=-24 color(white)(xxxxxxxx)A#
#color(white)(xxxxxxx)3xcolor(red)(-6y) =+12 color(white)(xxxxx.xxx)B#
#A xx 3:" "27xcolor(red)(+6y) =-72 color(white)(xxxxxxxx)C#
#B+C:" "30x =color(white)(xxx) -60#
#color(white)(xxxxxxxx)x =color(white)(xxxx) -2#

Substitute #-2 " for " x# in A
#color(white)(xxx) 9(-2) +2y =-24#
#color(white)(xxxx) -18 +2y =-24#
#color(white)(xxxxxxxxxx)2y =-24+18#
#color(white)(xxxxxxxxxx)2y =-6#
#color(white)(xxxxxxxxxxx)y =-3#