How do you solve the following system: #x-5y=-9, 6x+3y=-12#?

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Answer 1 · 2016-03-11T13:35:55

The solution for the system of equations is:
#color(blue)(x=-29/11#
#color(blue)(y = 14/ 11#

#x- 5y =-9# , multiplying by #6#
#color(blue)(6x)- 30y =-54#........equation #(1)#

#color(blue)(6x)+3y =-12#..........equation #(2)#

Solving by elimination.

Subtracting equation #(2)# from #(1)# results in elimination of #color(blue)(6x):#

#cancelcolor(blue)(6x)- 30y =-54#
#-cancelcolor(blue)(6x)-3y = 12#

#-33y = -42#

#y = (-cancel42) / (-cancel33)#

#color(blue)(y = 14/ 11#

Finding #x# from equation #1#:

#x- 5y =-9#

#x=-9 + 5y #

#x=-9 + 5 * (14/11)#

#x=-9 + 70/11#

#x=-99/11 + 70/11#

#color(blue)(x=-29/11#