How do you solve the following linear system: #3x-2y=7, 3x+4y=12#?

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Answer 1 · 2015-11-12T06:50:52

The solution for the system of equations is :
#color(blue)(y=5/6#

#color(blue)(x=(26)/(9)#

#color(blue)(3x)−2y=7#......equation #1#
#color(blue)(3x)+4y=12#......equation #2#

We can solve the system of equations by elimination

By subtracting equation #2# from #1# we can eliminate #color(blue)(3x#

#cancelcolor(blue)(3x)−2y=7#
#-cancelcolor(blue)(3x)-4y=-12#

#-6y=-5#

#y=(-5)/(-6)#

#color(blue)(y=5/6#

Now we substitute this value of #y# in equation #1# to find #x#:

#3x−2y=7#

#3x=7+2y#

#3x=7+cancel2*color(blue)(5/cancel6#

#3x=7+5/3#

#3x=(21+5)/3#

#3x=(26)/3#

#x=(26)/(3*3)#

#color(blue)(x=(26)/(9)#