How do you solve $6 m + n = 9$ $6m+n=9$ and $m - 8 n = 26$ $m-8n=26$ using substitution?

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How do you solve $6 m + n = 9$ $6m+n=9$ and $m - 8 n = 26$ $m-8n=26$ using substitution?

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Answer 1 · 2016-03-18T04:10:44

$m = 2$ $m=2$
$n = - 3$ $n=-3$

Explanation:

From the given equations
$6 m + n = 9$ $6m+n=9$ first equation
$m - 8 n = 26$ $m-8n=26$ second equation

Start with second equation
$m = 26 + 8 n$ $m=26+8n$
insert the equivalent in the first equation

$6 m + n = 9$ $6m+n=9$ first equation
$6 (26 + 8 n) + n = 9$ $6(26+8n)+n=9$ first equation
$156 + 48 n + n = 9$ $156+48n+n=9$
$49 n = 9 - 156$ $49n=9-156$
$49 n = - 147$ $49n=-147$
$n = - \frac{147}{49}$ $n=-147/49$
$n = - 3$ $n=-3$

Solve for m now using $n = - 3$ $n=-3$ and $m = 26 + 8 n$ $m=26+8n$

$m = 26 + 8 n$ $m=26+8n$
$m = 26 + 8 (- 3)$ $m=26+8(-3)$
$m = 26 - 24$ $m=26-24$
$m = 2$ $m=2$

check:using the original equations
$6 m + n = 9$ $6m+n=9$ first equation
$6 (2) + (- 3) = 9$ $6(2)+(-3)=9$ first equation

$12 - 3 = 9$ $12-3=9$
$9 = 9$ $9=9$

$m - 8 n = 26$ $m-8n=26$ second equation
$2 - 8 (- 3) = 26$ $2-8(-3)=26$ second equation
$2 + 24 = 26$ $2+24=26$
$26 = 26$ $26=26$

God bless....I hope the explanation is useful.

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How do you solve $6 m + n = 9$ $6m+n=9$ and $m - 8 n = 26$ $m-8n=26$ using substitution?

1 Answer

Explanation:

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How do you solve $6 m + n = 9$ $6m+n=9$ and $m - 8 n = 26$ $m-8n=26$ using substitution?