How do solve the following linear system?: # -x - y = 8 , 8x+2y=2 #?

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Answer 1 · 2016-03-13T13:23:50

The solution for the system of equations is:
# color(green)(x =3#
#color(green)(y = -11#

#-x-y=8# , multiplying this equation by #8#
#color(green)(-8x) -8y=64#..........equation #(1)#

#color(green)(8x) +2y =2#.................equation #(2)#

Solving by elimination would result in elimination of the terms #color(green)(8x)#:

Adding the two equations:

#cancelcolor(green)(-8x) -8y=64#
#cancelcolor(green)(8x) +2y =2#

#-6y =66#

#y = 66/(-6)#

#color(green)(y = -11#

Finding the value of #x# from equation #(1)#:
#-x-y=8#

# x =-y- 8#

# x =- color(green)((-11))- 8#

# x =11- 8#

# color(green)(x =3#