If m - n = 32 and 3m - 8n - 6 = 0, then what is 4m - 9n?

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Answer 1 · 2018-05-16T23:16:06

#4m-9n=38#

First, we solve for #m# in terms of #n#, using equation 1:

#m-n=32#

#color(blue)(m=n+32#

Next we substitute our solution for #m# in equation 2 to solve for #n#:

#3m-8n-6=0#

#3color(blue)((n+32))-8n-6=0#

#3n+96-8n-6=0#

#90-5n=0#

#90=5n#

#color(purple)(n=18)#

Now, we can solve equation 3 without ever getting the discrete solution for #m#:

#4color(blue)(m)-9color(purple)(n)=x#

#4color(blue)((color(purple)(n)+32))-9color(purple)(n)=x#

#4color(purple)(n)+128-9color(purple)(n)=x#

#128-5color(purple)(n)=x#

#128-5color(purple)((18))=x#

#128-90=x#

#color(green)(x=38)#