How do you solve using elimination of #3x+6y=12# and #2x-2.5y=13#?

1 Answer
Nov 7, 2015

Answer:

The system has one dolution: #{(x=5 7/13),(y=-10/13):}#

Explanation:

The original system is:

#{(3x+6y=12),(2x-2.5y=13):}#

The elimination method means to change the system so that it is possible to eliminate one variable by adding (or substracting) both sides of the equations:

First we can divide both sides of the first equation by #3# to make all the coefficients smaller and multiply the second equation by #2# to make all the coefficients integer:

#{(x+2y=4),(4x-5y=26):}#

Now if we multiply the first equation by #(-4)# the coefficients of #x# will be opposite numbers (#4# and #-4#)

#{(-4x-8y=-16),(4x-5y=26):}#

Now if we add both sides of the equations the variable #x# will be eliminated:

#-13y=10#

#y=-10/13#

Now if we move #2y# to the right side of the first equation before the last multiplication we get:

#x=4-2y#

Now we only have to put calculated #y# in this equation and calculate #x#

#x=4-2*(-10/13)#

#x=4+20/13#

#y=(52+20)/13#

#y=72/13#

#y=5 7/13#