Determine which ordered pairs satisfy the given equation. \[ 3 x-5 y=1 \quad\left(\frac{1}{3}, 0\right)(7,4)(0,-2) \] Select all ordered pairs that satisfy the given equation. A. $\left(\frac{1}{3}, 0\right)$ B. $(7,4)$ C. $(0,-2)$ D. None of the ordered pairs satisfy the equation.

Step 1 ：Given the equation \(3x - 5y = 1\), we need to determine which ordered pairs satisfy this equation. The ordered pairs given are \(\left(\frac{1}{3}, 0\right)\), \((7,4)\), and \((0,-2)\).

Step 2 ：First, we substitute the values of the first ordered pair into the equation. For \(\left(\frac{1}{3}, 0\right)\), \(x = \frac{1}{3}\) and \(y = 0\). Substituting these values into the equation, we find that the equation holds true.

Step 3 ：Next, we substitute the values of the second ordered pair into the equation. For \((7,4)\), \(x = 7\) and \(y = 4\). Substituting these values into the equation, we find that the equation holds true.

Step 4 ：Finally, we substitute the values of the third ordered pair into the equation. For \((0,-2)\), \(x = 0\) and \(y = -2\). Substituting these values into the equation, we find that the equation does not hold true.

Step 5 ：From the above steps, we can conclude that the ordered pairs that satisfy the equation \(3x - 5y = 1\) are \(\boxed{\left(\frac{1}{3}, 0\right)}\) and \(\boxed{(7,4)}\).