How do you solve #9m+n=35# and #m-9n=13# using substitution?

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Answer 1 · 2016-03-21T17:02:19

The solution for the system of equations is:
#color(blue)(m=4#
#color(blue)(n=-1#

#9m + n =35#............equation #(1)#

#m - 9n =13#
#color(blue)(m =13 + 9n #.............equation #(2)#

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

#9m + n =35#

#9 * (color(blue)(13 + 9n )) + n =35#

#(9 * 13) + (9 * 9n) + n =35#

#117 + 81n + n =35#

# 82n =35- 117 #

# 82n =- 82 #

#n = (-82) / 82#

#color(blue)(n=-1#

Finding the value of #m# from equation #(2)#:

#m =13 + 9n #

#m =13 + 9 * (-1)#

#m =13 - 9 #

#color(blue)(m=4#