If `x=2t and y=(2t-1)/(3)`, then for what value of `t, x=y` is correct?

Options

A. `(1)/(3)`
B. `-(1)/(4)`
C. `(1)/(4)`
D. `-(1)/(2)`

Answer

To solve the problem where \( x = 2t \) and \( y = \frac{2t - 1}{3} \), we need to find the value of \( t \) for which \( x = y \).

### Step-by-Step Solution:

1. **Set the equations equal to each other**:
\[ 2t = \frac{2t - 1}{3} \]

2. **Eliminate the fraction**:
To eliminate the fraction, multiply both sides by 3:
\[ 3 \cdot (2t) = 2t - 1 \]
This simplifies to:
\[ 6t = 2t - 1 \]

3. **Rearrange the equation**:
Subtract \( 2t \) from both sides:
\[ 6t - 2t = -1 \]
This simplifies to:
\[ 4t = -1 \]

4. **Solve for \( t \)**:
Divide both sides by 4:
\[ t = \frac{-1}{4} \]

### Final Answer:
The value of \( t \) for which \( x = y \) is:
\[ t = -\frac{1}{4} \]