To solve the given equation for [tex]\( y \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
2x + 3y = -9
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex].
Subtract [tex]\( 2x \)[/tex] from both sides of the equation to keep the [tex]\( y \)[/tex] term on one side:
[tex]\[
3y = -9 - 2x
\][/tex]
3. Solve for [tex]\( y \)[/tex].
We need [tex]\( y \)[/tex] by itself, so divide both sides of the equation by 3:
[tex]\[
y = \frac{-9 - 2x}{3}
\][/tex]
Thus, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = \frac{-9 - 2x}{3}
\][/tex]
To verify the result with a sample value, let's take [tex]\( x = 1 \)[/tex]:
Substitute [tex]\( x = 1 \)[/tex] into the equation:
[tex]\[
y = \frac{-9 - 2(1)}{3}
\][/tex]
Simplify the expression:
[tex]\[
y = \frac{-9 - 2}{3} = \frac{-11}{3} = -3.6666666666666665
\][/tex]
Therefore, for [tex]\( x = 1 \)[/tex], [tex]\( y = -3.6666666666666665 \)[/tex].
The expression for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = \frac{-9 - 2x}{3}
\][/tex]
This expression allows you to calculate [tex]\( y \)[/tex] for any given [tex]\( x \)[/tex].
