How do you solve the system #2x-9y=6# and #4x-3y=-7#?

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Answer 1 · 2015-07-24T14:02:58

The solution for the system of equations is:
#color(blue)(x=-27/10, y=-19/15#

#2x−9y=6#, multiplying this equation by #2#

#color(blue)(4x)−18y=12#........equation #(1)#

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

Solving through elimination:

Subtracting equation #(1)# from #(2)#:
# color(blue)(cancel(4x)−3y=−7#
#color(blue)(cancel(-4x)+18y=-12#

#15y=-19#

#color(blue)(y=-19/15#

Finding #x# from the first equation :

#2x−9y=6#

#2x=6+9y#

#x=(6+9y)/2#

#x=(6+9*(-19/5))/2#

#color(blue)(x=-27/10#