How do you solve using the addition method and determine if the system is independant, dependant, inconsistant given 3/7x+5/9y=27 and 1/9x+2/7y=7?

1 Answer
Feb 6, 2017

Answer:

#x=63# and #y=0#. The system is consistent and the equations are independent.

Explanation:

The system of equations is

#3/7x+5/9y=27#
#1/9x+2/7y=7#

Multiply the first equation by #-7"/"21# to eliminate #x#

#-7/27(3/7x+5/9y)=-7/27(27)#
#1/9x+2/7y=7#

This gives

#-1/9x-35/243y=-7#
#" "1/9x+2/7y" "=7#

Adding them together gives

#241/1701y=0 => y=0#

Plug #y=0# back into either of the original equations for #x#

#3/7x+5/9(0)=27#
#3/7x=27#
#x=27(7/3)#
#x=63#

If the lines intersect, then the system has one solution, given by the point of intersection. The system is consistent and the equations are independent.

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