Certainly! Let's solve the given equation for [tex]\( y \)[/tex] step-by-step when the value of [tex]\( x \)[/tex] is [tex]\(-10\)[/tex].
The given equation is:
[tex]\[
2x - 9y = -38
\][/tex]
1. Substitute [tex]\( x = -10 \)[/tex] into the equation:
[tex]\[
2(-10) - 9y = -38
\][/tex]
2. Simplify the equation:
[tex]\[
-20 - 9y = -38
\][/tex]
3. Isolate the term involving [tex]\( y \)[/tex]:
Add 20 to both sides of the equation to move the constant term to the right side:
[tex]\[
-9y = -38 + 20
\][/tex]
Simplify the right side:
[tex]\[
-9y = -18
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
Divide both sides of the equation by [tex]\(-9\)[/tex]:
[tex]\[
y = \frac{-18}{-9}
\][/tex]
Simplify the fraction:
[tex]\[
y = 2
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = -10 \)[/tex] is:
[tex]\[
y = 2
\][/tex]
