$\begin{array}{l}y=2 x^{2}-x+3 \\ y=x^{2}+5 x-6\end{array}$

Step 1 ：Set the two equations equal to each other: \(2x^{2} - x + 3 = x^{2} + 5x - 6\)

Step 2 ：Simplify the equation: \(x^{2} - 6x + 9 = 0\)

Step 3 ：Solve for x: \(x = 3\)

Step 4 ：Final Answer: The solution to the system of equations is \(\boxed{3}\)