To determine the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] in the equation [tex]\( 3x - 4y = 65 \)[/tex], let's follow these steps:
1. Substitute the given value of [tex]\( y \)[/tex] into the equation.
The equation given is:
[tex]\[
3x - 4y = 65
\][/tex]
Substitute [tex]\( y = 4 \)[/tex]:
[tex]\[
3x - 4(4) = 65
\][/tex]
2. Simplify the equation.
Calculate [tex]\( 4 \times 4 \)[/tex]:
[tex]\[
4(4) = 16
\][/tex]
Now substitute back in:
[tex]\[
3x - 16 = 65
\][/tex]
3. Isolate the term involving [tex]\( x \)[/tex].
To isolate [tex]\( 3x \)[/tex], add 16 to both sides of the equation:
[tex]\[
3x - 16 + 16 = 65 + 16
\][/tex]
This simplifies to:
[tex]\[
3x = 81
\][/tex]
4. Solve for [tex]\( x \)[/tex].
Divide both sides of the equation by 3:
[tex]\[
x = \frac{81}{3}
\][/tex]
Simplify the right-hand side:
[tex]\[
x = 27
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( \boxed{27} \)[/tex].
