Question - Determining the Value of an Exponential Expression Given a Linear Equation
Solution:
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:$$ A ) 9 $$
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