How do you solve the system of equations #x+2y = 8# and #3x-4y = 4# using substitution?

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Answer 1 · 2016-05-09T15:14:04

The solution for the system of equations is:
#color(blue)(x=4#
# color(blue)(y = 2 #

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

#3x - 4y = 4#...........equation #(2)#

Substituting equation #1# in #2#:

#3x - 4y = 4#

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

# 24 - 6y - 4y = 4#

# - 10y = 4 - 24 #

# - 10y = - 20 #

# y = (- 20) / (-10) #

# color(blue)(y = 2 #

Finding #x# from equation #1:#
#x = 8 - 2y#

#x = 8 - 2 * color(blue)(2)#

#x = 8 - 4#

#color(blue)(x=4#