How do you solve #8m + n = 34# and #m - 4n = 29# using substitution?

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Answer 1 · 2016-04-18T17:11:55

The solution for the system of equations is:
#color(blue)(m=5#
# color(blue)(n = - 6#

#8m + n = 34#..............equation #(1)#

#m - 4n = 29 #
#color(green)(m = 29 + 4n #..............equation #(2)#

Substituting equation #2# in #1#

#8m + n = 34#

#8 * (color(green)( 29 + 4n )) + n = 34#

#232 + 32n + n = 34#

# 33n = 34 - 232 #

# 33n = - 198#

# n = - 198/33#

# color(blue)(n = - 6#

Finding #m# from equation #1#:
#8m + n = 34#

#8m = 34 - n #

#8m = 34 - (-6) #

#8m = 34 + 6 #

#8m = 40 #

#m = 40 / 8#

#color(blue)(m=5#