How do you solve the following system?: # 2x + 7y = -8, x - 2y = 7 #

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Answer 1 · 2018-04-21T14:52:47

#x = 3# and #y = -2#

#2x + 7y = -8 color(white)(....) ——(1)#
#x - 2y = 7 color(white)(....) ——(2)#

Multiply second equation by #2#
#2x - 4y = 14 color(white)(....) ——(3)#

Subtract #3#nd equation from #1#st

#2x + 7y - (2x - 4y) = -8 - 14#

#2x + 7y - 2x + 4y = -22#

#11y = -22#

#y = -22/11#

#y = -2#

Substitute #y = -2# in equation #(1)#

#2x + (7 × -2) = -8#

#2x - 14 = -8#

#2x = 14 - 8#

#2x = 6#

#x = 6/2#

#x = 3#