To find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] equals 15 in the equation [tex]\( -x - 9y = 39 \)[/tex], follow these steps:
1. Substitute [tex]\( x \)[/tex] with 15 in the equation:
[tex]\[
-15 - 9y = 39
\][/tex]
2. Combine like terms by adding 15 to both sides of the equation to isolate the term involving [tex]\( y \)[/tex] on one side:
[tex]\[
-15 + 15 - 9y = 39 + 15
\][/tex]
This simplifies to:
[tex]\[
-9y = 39 + 15
\][/tex]
Therefore,
[tex]\[
-9y = 54
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing both sides of the equation by -9:
[tex]\[
y = \frac{54}{-9}
\][/tex]
4. Simplify the fraction on the right-hand side:
[tex]\[
y = -6
\][/tex]
Hence, the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] equals 15 is [tex]\( y = -6 \)[/tex].
