How do you solve the following system?: #6x +5y =-1 , -5x -9y = 5#

1 Answer
Jatin Trivedi
Mar 24, 2018

#x = 16/29#
#y = -25/29#

Explanation:

For solving using substitution method you have to separate out the value of any one variable #(x or y)# in any of the equation and put it in the other equation.
Assuming #6x + 5y = -1# to be equation #1 # and #-5x - 9y = 5# be equation #2#
Seperating out the value of #x#
#x = (-1 - 5y)/6# and now putting it in the second equation
#-5((-1-5y)/6) - 9y = 5#
#5((1+5y)/6) - 9y = 5#
#((5 + 25y)/6) - 9y = 5#
Now on taking #LCM# on LHS
#((5 + 25y - 54y)/6) = 5#
#(5 + 25y - 54y) = 30#
#5 - 29y = 30#
#29y = -25#
#y = -25/29#
Now put the value of #y# in any of the two equations
#(6x + 5(-25/29)) = -1#
#(6x -125/29) = -1#
#6x = 125/29 - 1#
#6x = (125-29)/29#
#6x = 96/29#
#x = 16/29#

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