How do you solve x + y = 23 and y = x - 5?

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Answer 1 · 2016-02-15T18:05:46

#x=14 and y=9#

Since #y=x-5# in the second equation, we may substitute this fact into the first equation and then solve for #x#.
Doing so we get :

#x+(x-5)=23#

#therefore 2x=28#

#therefore x=14#.

Now back-substitute to get #y=14-5=9#.

Answer 2 · 2016-02-15T18:08:37

The solution for the system of equations is:
#color(blue)(x=14#

#color(blue)(y=9#

#x+y=23#.......equation #1#
#x-y=5#..........equation #2#

Solving by elimination.

Adding equations #1# and #2#

#x+cancelcolor(blue)(y)=23#
#x-cancelcolor(blue)(y)=5#

#2x=28#

#x=28/2#

#color(blue)(x=14#

Finding #y# from equation #1#:
#x+y=23#

#y=23-x#

#y=23-14#

#color(blue)(y=9#