How do you solve the following system?: # 8x - 2y = - 4 , x + 2y = 6 #

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Answer 1 · 2016-04-13T16:04:51

The solution is:
#x = 2/ 9#

#y = 26/ 9 #

#8x color(blue)(- 2y) = -4#..........equation #(1)#

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

Solving by elimination:

Adding equations #(1)# and #(2)#

#8x color(blue)cancel(- 2y) = -4#

#x + cancelcolor(blue)( 2y) =6#

#9x = 2#

#x = 2/ 9#

Finding #y# by substituting the value #x# in equation #1#
#8x color(blue)(- 2y) = -4#

#8 * (2/9) color(blue)(- 2y) = -4#

#16/9 + 4 = 2y #

#16/9 + 36/9 = 2y #

#52/9 = 2y #

#52/(9 * 2 ) =y #

#y = cancel 52/( cancel18) #

#y = 26/9 #