How do you solve the following system?: # -2y=2x+6 , -x-8y=32 #

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Answer 1 · 2016-03-26T14:20:47

The solution for the system of equations is:
# color(blue)( x = 8/7#
#color(blue)(y = -29 / 7#

#-2y = 2x +6#
#color(blue)(2x) + 2y = -6#..........equation #(1)#

#-x -8y =32# , multiplying by #2#
#color(blue)(-2x) -16y =64# .....equation #(2)#

Solving by elimination:

Adding equations #1# and #2#:

#cancelcolor(blue)(2x) + 2y = -6#
#cancelcolor(blue)(-2x) -16y =64#

#-14y = 58#

#y = 58 / (-14)#

#color(blue)(y = -29 / 7#

Finding #x# from equation #2#:
#-x -8y =32#

# -8y - 32 = x#

# -8 * color(blue)(( 29 / (-7))) - 32 = x#

# 232/7 - 32 = x#

# 232/7 - 224/7 = x#

# color(blue)( x = 8/7#

The solution for the system of equations is:
# color(blue)( x = 8/7#
#color(blue)(y = -29 / 7#