How do you solve the system #x+y=7# and #2x-y=2# by addition?

1 Answer
Mar 27, 2016

Answer:

#(x,y)=(3,4)#

Explanation:

Given
#color(white)("XXX")color(red)(x+y)=color(red)(7)#
#color(white)("XXX")color(blue)(2x-y)=color(blue)(2)#

Adding the two equations together
#color(white)("XXX")color(red)(x)+color(blue)(2x)+color(red)(y)+color(blue)((-y))=color(red)(7)+color(blue)(2)#

#color(white)("XXX")3x = 9#

#color(white)("XXX")x=3#

The we can substitute #3# for #x# in #color(blue)(2x-y=2)#
to get
#color(white)("XXX")2(3)-y=2#

#color(white)("XXX")6-y=2#

#color(white)("XXX")y=4#