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

$4 m - 9 n = 38$ $4m-9n=38$

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

$m - n = 32$ $m-n=32$

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

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

$3 m - 8 n - 6 = 0$ $3m-8n-6=0$

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

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

$90 - 5 n = 0$ $90-5n=0$

$90 = 5 n$ $90=5n$

$n = 18$ $color(purple)(n=18)$

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

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

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

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

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

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

$128 - 90 = x$ $128-90=x$

$x = 38$ $color(green)(x=38)$