How do you determine the solution in terms of a system of linear equations for #-5x-5y=5#, #-40x-3y=2#?

1 Answer
May 18, 2018

Answer:

#x=1/37# and #y=-38/37#

Explanation:

#-5x-5y=5#
#-40x-3y=2#

Lets cancel out the #y# terms to find #x#. Multiply the top equation by #-3# and the bottom equation by #-5# (multiply equations by opposite coefficients of #y#):

#(-5x*-3)-(5y*-3)=5*-3#
#(-40x*-5)-(3y*-5)=2*-5#

#15x+15y=-15#
#200x+15y=-10#

Subtract them from each other to eliminate #y#:

#-185x= -5#
#x=-5/-185#
#x=1/37#

Substitute #x=1/37# back into one of the original equations (e.g. #-5x-5y=5#) to find #y#:

#-5(1/37)-5y=5#
#(-5/37)-5y=5#
#-5y=5+(5/37)#
#-5y=190/37#
#y=(190/37)/-5#
#y=-38/37#

Double check your results by substituting both values of #x# and #y# into an original equation and see whether the result is correct.