1. The problem is to simplify the expression $y = \frac{1}{3} - \frac{2}{7} \times \frac{5}{4}$. 2. According to the order of operations, multiplication must be done before subtraction. 3. Multiply the fractions $\frac{2}{7}$ and $\frac{5}{4}$: $$\frac{2}{7} \times \frac{5}{4} = \frac{2 \times 5}{7 \times 4} = \frac{10}{28}$$ 4. Simplify $\frac{10}{28}$ by dividing numerator and denominator by their greatest common divisor 2: $$\frac{\cancel{10}^{5}}{\cancel{28}^{14}} = \frac{5}{14}$$ 5. Now subtract $\frac{5}{14}$ from $\frac{1}{3}$: $$y = \frac{1}{3} - \frac{5}{14}$$ 6. Find a common denominator for $3$ and $14$, which is $42$: $$\frac{1}{3} = \frac{14}{42}, \quad \frac{5}{14} = \frac{15}{42}$$ 7. Perform the subtraction: $$y = \frac{14}{42} - \frac{15}{42} = \frac{14 - 15}{42} = \frac{-1}{42}$$ 8. The simplified value of $y$ is: $$y = -\frac{1}{42}$$