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

Given equation: $6x - 4y = 3$

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

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

Now, calculate each term:

1. $6 \times \frac{4}{3} = 2 \times 4 = 8$
2. $4 \times \frac{5}{4} = 5$

So, the equation becomes:

$8 - 5 = 3$

Since $3 = 3$, the equation holds true.

Therefore, the ordered pair $\left(\frac{4}{3}, \frac{5}{4}\right)$ is a solution to the equation $6x - 4y = 3$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can substitution help in solving systems of equations?
2. What happens if an ordered pair does not satisfy the equation?
3. How would you solve the equation $6x - 4y = 3$ for $x$?
4. Can an ordered pair satisfy multiple linear equations simultaneously?
5. What is the importance of checking multiple points in a linear equation?

Tip: When substituting fractions, simplifying the equation step by step helps in avoiding errors.