Determining the Value of an Exponential Expression Given a Linear Equation
Given: \( 6z - 4y = 8 \)
We need to find the value of \( \frac{27z}{9y} \)
First, solve for \( z \) in terms of \( y \):
\( z = \frac{8}{6} + \frac{4y}{6} \)
\( z = \frac{4}{3} + \frac{2y}{3} \)
Now, substitute \( z \) into the expression \( \frac{27z}{9y} \):
\( \frac{27(\frac{4}{3} + \frac{2y}{3})}{9y} \)
\( \frac{27 \times \frac{4}{3}}{9y} + \frac{27 \times \frac{2y}{3}}{9y} \)
\( \frac{36}{9y} + \frac{18y}{9y} \)
\( \frac{36}{9y} + 2 \)
Now, note that the second part of the expression is independent of \( y \), and the first part's numerator is not a multiple of \( y \) (since \( y \neq 0 \)), hence it cannot simplify to a constant. Therefore, the answer must be an integer that is 2 plus a positive number or 2 itself.
Among the options given, only \( 9 \) satisfies this condition, since it's 7 more than 2.
Thus the correct option is:
\( A ) 9 \)
