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 $m$ :

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

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

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

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

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

$128-90=x$

$color(green)(x=38)$