How do you solve #3x+y=16# and #2x+y=11#?

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Answer 1 · 2015-06-30T03:59:25

The solutions are:
#color(blue)(x=5#
# color(blue)(y = 1#

#3x+color(green)(y)=16 # ........equation #(1)#

#2x+color(green)(y)=11#..........equation #(2)#

These equations can be solved through elimination :
(by eliminating #color(green)(y#)

Subtracting equation #(2)# from equation #(1)# :

#3x+cancelcolor(green)(y)=16 #

#-2x-cancelcolor(green)(y)=-11#

#color(blue)(x=5#

Now , finding #y#, from equation #1# :

#y = 16 -3x#
# = 16 - 3.(5)#
# color(blue)(y = 1#