Solve the following system with non-linear functions algebraically. \[ \begin{array}{l} y=x \\ y=8 x^{1 / 2}-15 \end{array} \] Round your answer(s) to two decimal places. There are two solutions and they are: \[ \left(x_{1}, y_{1}\right)=(\square, \square) \text { or }\left(x_{2}, y_{2}\right)=(\square, \square) \] There is one solution and it is: \[ \left(x_{1}, y_{1}\right)=(\square, \square) \] There is no solution.

Step 1 ：The system of equations is non-linear. To solve it, we can set the two equations equal to each other and solve for x. Then, we can substitute x into one of the equations to find y.

Step 2 ：Setting the equations equal to each other gives us the equation \(x = 8 \sqrt{x} - 15\).

Step 3 ：Solving this equation gives us two solutions for x: \(x_{1} = 9\) and \(x_{2} = 25\).

Step 4 ：Substituting these values back into the equation \(y = x\) gives us corresponding y values: \(y_{1} = 9\) and \(y_{2} = 25\).

Step 5 ：\(\boxed{\text{Final Answer: The solutions to the system of equations are } (x_{1}, y_{1})=(9, 9) \text{ and } (x_{2}, y_{2})=(25, 25)}\)