How do solve the following linear system?: # -6x-2y=-8 , 3x – 4y = 7 #?

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Answer 1 · 2016-04-26T14:52:03

The solution for the system of equations is:
#color(blue)(x = 23/(15) #

#color(blue)(y = -3/5#

# color(green)(- 6x) - 2y = - 8 # ......equation #(1)#

#3x - 4y = 7#, multiplying by #2#
#color(green)(6x) - 8y = 14#...............equation #(2)#

Solving by elimination:

Adding equations #1# and #2# eliminates #color(green)(6x.#

# cancelcolor(green)(- 6x) - 2y = - 8 #
#cancelcolor(green)(6x) - 8y = 14#

#-10y = 6#

#y = - 6/10#

#color(blue)(y = -3/5#

Finding #x# from equation # 2#:
#3x - 4y = 7#

#3x = 7 + 4y#

#3x = 7 + 4 * color(blue)((-3/5)#

#3x = 7 - 12/5#

#3x = 35/5 - 12/5#

#3x = 23/5 #

#x = 23/(5 * 3) #

#color(blue)(x = 23/(15) #