How do you solve #3x-7y=-13# and #-2x+3y=7#?

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Answer 1 · 2015-08-03T08:26:57

The solutions for the system of equations are
#color(blue)(x=-2,y=1#

#3x−7y=−13#, Multiplying this equation with #2#
#color(blue)(6x)−14y=-26#......equation #(1)#

# −2x+3y=7#, Multiplying this equation with #3#
# −color(blue)(6x)+9y=21#.......equation #(2)#

Solving through elimination

Adding the two equations results in elimination of #color(blue)(6x#
#cancel(6x)−14y=-26#

# cancel(−6x)+9y=21#

#-5y=-5#
#color(blue)(y=1#

Now, we find #x# by substituting #y# in equation #(1)#
#3x−7y=−13#

#3x−7*1=−13#

#3x=−13+7#

#x=-6/3#

#color(blue)(x=-2#