How do you solve this system of equations: #6x + 5y = 300 and 3x + 7y = 285#?

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Answer 1 · 2018-05-20T02:15:58

#x=25#
#y=30#

#6x + 5y = 300#
#3x + 7y = 285#

Using elimination we need to find a common denominator of the coefficient of either x or y; this one looks like x is easier:

LCD of 6 and 3 is 6 so let's multiply the second equation by #-2#:

#-2(3x + 7y = 285)#

#-6x -14y = -570#

now add the equations together:

#" "6x + 5y = 300#
#-6x -14y = -570#

#-9y = -270#

#y=30#

insert y into either of the original equations to solve for x:

#3x + 7y = 285#

#3x + 7(30)= 285#

#x=25#