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How do you solve the following linear system: # -x + y = 3, x + y = 5 #?

1 Answer

Apr 16, 2018

#x=1 and y=4#

Explanation:

Note that the two #x#-terms are additive inverses, so if you add the two equations, the #x#-terms will be eliminated:

#" "color(blue)(-x)+y = 3" "....... A#
#" "color(blue)(+x)+y = 5" "......."B#

#A+B:" "2y =8#
#color(white)(xxxxx.xxx) y=4#

Substitute #y=4# into equation #B# to get #x=1#

Checking in both equations gives:

#-1+4=3#
#+1+4=5#

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