How do you solve #3x + 7y = 18# and #x + 2y = 5#?

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Answer 1 · 2016-06-14T02:25:18

The solution for the system of equations is:

#color(green)(x=-1#

#color(green)(y = 3#

#3x + 7y = 18#........equation #(1)#

#x + 2y = 5#
#color(blue)(x = 5 - 2y #.............equation #(2)#

Substituting equation #2# in equation #1:#

#3x + 7y = 18#

#3 xx (color(blue)( 5 - 2y)) + 7y = 18#

#15 - 6y + 7y = 18#

#15 + y = 18#

#y = 18 - 15 #

#color(green)(y = 3#

Now we substitute the value of #y# in equation #2# to find #x:#

#color(blue)(x = 5 - 2y #

#x = 5 - 2 xx (3) #

#x = 5 - 6 #

#color(green)(x=-1#