How do you solve 2x+3y=2 and 6x+18y=9?

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Answer 1 · 2015-09-05T07:43:52

The solution is
#color(blue)(x=1/2, y=1/3#

#2x+3y=2 #, multiplying this equation by #3#
#color(blue)(6x)+9y=6 #......equation #1#

#color(blue)( 6x)+18y=9#.....equation #2#

Solving by elimination.
Subtracting equation #2# from #1# eliminates #color(blue)(6x#

#cancelcolor(blue)(6x)+9y=6 #
#-cancelcolor(blue)( 6x)-18y=-9#

#-9y=-3#
#color(blue)(y=1/3#

Finding #x# by substituting #y# in equation #1#:

#2x+3y=2 #

#2x=2 -3y#

#2x=2 -3*1/3#

#2x=2 -1#

#2x=1#
#color(blue)(x=1/2#