To determine the value of [tex]\( x \)[/tex] in the equation [tex]\( 3x - 4y = 65 \)[/tex] given [tex]\( y = 4 \)[/tex], let's follow these steps:
1. Substitute [tex]\( y = 4 \)[/tex] into the equation:
The given equation is:
[tex]\[
3x - 4y = 65
\][/tex]
2. Replace [tex]\( y \)[/tex] with 4:
[tex]\[
3x - 4(4) = 65
\][/tex]
3. Simplify the equation:
[tex]\[
3x - 16 = 65
\][/tex]
4. Isolate the term with [tex]\( x \)[/tex]:
Add 16 to both sides of the equation:
[tex]\[
3x - 16 + 16 = 65 + 16
\][/tex]
[tex]\[
3x = 81
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Divide both sides by 3:
[tex]\[
x = \frac{81}{3}
\][/tex]
[tex]\[
x = 27
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( \boxed{27} \)[/tex].
