To determine whether the given ordered pair $\left(\frac{5}{3}, \frac{1}{4}\right)$ is a solution of the equation $6x - 4y = -4$, we can substitute $x = \frac{5}{3}$ and $y = \frac{1}{4}$ into the equation and see if the equation holds true.

Given equation: $6x - 4y = -4$

Substitute $x = \frac{5}{3}$ and $y = \frac{1}{4}$ into the equation:

$6\left(\frac{5}{3}\right) - 4\left(\frac{1}{4}\right) = -4$

Now, calculate each term:

1. $6 \times \frac{5}{3} = 2 \times 5 = 10$
2. $4 \times \frac{1}{4} = 1$

So, the equation becomes:

$10 - 1 = 9$

Since $9 \neq -4$, the equation does not hold true.

Therefore, the ordered pair $\left(\frac{5}{3}, \frac{1}{4}\right)$ is not a solution to the equation $6x - 4y = -4$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you determine if an ordered pair is a solution to a linear equation?
2. Can you graphically interpret the result of this problem?
3. What is the geometric meaning of a solution to a linear equation?
4. How would you solve the equation $6x - 4y = -4$ for $y$?
5. What would happen if you substituted another pair into the equation?

Tip: Always check your calculations carefully when substituting values to avoid simple errors.