If we add $1$ to the numerator and subtract $1$ from the denominator, a fraction reduces to $1$. Form a linear equation for this information.

Identify whether $\left(4, 3\right)$ is the solution of the linear equation $3y-2x=1$.$$

Identify whether $\left(2\sqrt{2}, 3\sqrt{2}\right)$ is the solution of the linear equation $3y-2x=1$.$$