Solve the system: $y=\frac{2}{3}x-1$ and $3x+2y=7$. Provide the intersection point.

$(2,0)$ which satisfies neither original equation simultaneously and reflects a calculation error.

$(3,1)$ which would be a rounded estimate from an imprecise graph but not the exact algebraic intersection.

$(\frac{9}{13},-\frac{2}{13})$ which results from a sign error during substitution and algebraic simplification.

$(\frac{27}{13},\frac{5}{13})$