To find the value of [tex]\( m \)[/tex] given that [tex]\((-2, m)\)[/tex] is a solution of the equation [tex]\( 3x - 2y = s \)[/tex], we can follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the equation:
The equation given is [tex]\( 3x - 2y = s \)[/tex].
Substituting [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2) - 2y = s \][/tex]
2. Simplify the equation:
[tex]\[ -6 - 2y = s \][/tex]
3. Isolate [tex]\( y \)[/tex] (which is represented as [tex]\( m \)[/tex] in the coordinates):
[tex]\[ -2y = s + 6 \][/tex]
4. Solve for [tex]\( y \)[/tex] (or [tex]\( m \)[/tex]):
[tex]\[
y = -\frac{s + 6}{2}
\][/tex]
Thus,
[tex]\[
m = -\frac{s + 6}{2}
\][/tex]
5. Given value of [tex]\( s \)[/tex]:
From the problem or context, we know after substituting [tex]\( x = -2 \)[/tex], [tex]\( s \)[/tex] was found to be [tex]\(-6\)[/tex].
6. Substitute [tex]\( s = -6 \)[/tex] into the solved expression for [tex]\( m \)[/tex]:
[tex]\[
m = -\frac{-6 + 6}{2}
\][/tex]
7. Simplify the expression:
[tex]\[
m = -\frac{0}{2}
\][/tex]
[tex]\[
m = 0
\][/tex]
Thus, the value of [tex]\( m \)[/tex] is [tex]\( 0 \)[/tex].
