To find the value of \( x \), we first need to express \( x \) in terms of \( y \) based on the information provided.
We know two relationships involving \( y \):
- \( x = \frac{2}{7}y \)
- \( \frac{5}{9} = \frac{3}{4}y \)
From the second equation, we need to solve for \( y \):
\[ \frac{5}{9} = \frac{3}{4}y \]
To eliminate the fraction, we can cross-multiply:
\[ 5 \times 4 = 9 \times 3y \]
This simplifies to:
\[ 20 = 27y \]
Now, we can solve for \( y \):
\[ y = \frac{20}{27} \]
Now, we can substitute this value of \( y \) back into the equation for \( x \):
\[ x = \frac{2}{7}y = \frac{2}{7} \times \frac{20}{27} \]
Calculating \( x \):
\[ x = \frac{2 \times 20}{7 \times 27} = \frac{40}{189} \]
Thus, the value of \( x \) is
\[ \boxed{\frac{40}{189}} \]
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