How do you solve $2 m - 3 n = 6$ $2m - 3n = 6$ and $m = 3 - 2 n$ $m = 3 - 2n$ using substitution?

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Answer 1 · 2016-03-15T16:26:53

The solution for the system of equations is:
$n = 0$ $color(blue)(n=0$
$m = 3$ $color(blue)(m=3$

$2 m - 3 n = 6$ $2m−3n=6$ ..............equation $(1)$ $(1)$
$m = 3 - 2 n$ $color(green)( m=3−2n )$ .................equation $(2)$ $(2)$

Substituting equation $2$ $2$ in $1$ $1$ :

$2 m - 3 n = 6$ $2m−3n=6$

$2 \cdot (3 - 2 n) - 3 n = 6$ $2 * color(green)( (3−2n ))−3n=6$

$6 - 4 n - 3 n = 6$ $6 -4n−3n=6$

$6 - 7 n = 6$ $6 -7n=6$

$6 - 6 = 7 n$ $6 - 6 = 7n$

$7 n = 0$ $7n=0$

$n = \frac{0}{7}$ $n=0/7$

$n = 0$ $color(blue)(n=0$

finding the value of $m$ $m$ by substituting the value of $n$ $n$ in equation $2$ $2$ :

$m = 3 - 2 n$ $m=3−2n$

$m = 3 - 2 \cdot 0$ $m=3−2 * 0$

$m = 3 - 0$ $m=3- 0$

$m = 3$ $color(blue)(m=3$

How do you solve 2m−3n=62m - 3n = 6 and m=3−2nm = 3 - 2n using substitution?