How do you solve #5m+n=39# and #m-3n=27# using substitution?

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Answer 1 · 2016-03-28T16:42:15

The solution for the system of equations is:
#color(green)(m = 9 #
# color(green)(n =-6)#

#5m + n =39#..................equation #(1)#

#m - 3n = 27 #
#color(green)(m = 27 + 3n #..................equation #(2)#

Substituting equation #(2)# in #(1)#

#5m + n =39#

#5 * (color(green)( 27 + 3n)) + n =39#

#5 * (color(green)( 27 )) + 5 * color(green)(( 3n)) + n =39#

#135 + 15n+ n =39#

#135 + 16n =39#

# 16n =-96#

# n =-96/ (16)#

# color(green)(n =-6)#

Finding #m# by substituting the value of #n# in equation #(2)#:
#m = 27 + 3n #

#m = 27 + 3 * (-6) #

#m = 27 - 18 #

#color(green)(m = 9 #