Solve the system of equations. \[ \begin{array}{l}y=-37 x-39 \\ y=x^{2}-21 x+25\end{array} \] Write the coordinates in exact form. Simplify

We start with the system of equations: \[ \begin{aligned} y &= -37x - 39,\\[6mm] y &= x^2 - 21x + 25. \end{aligned} \] Since both expressions equal \( y \), we set them equal to each other: \[ x^2 - 21x + 25 = -37x - 39. \] Step 1. Rearrange the equation to bring all terms to one side: \[ x^2 - 21x + 25 + 37x + 39 = 0. \] Step 2. Combine like terms: \[ x^2 + 16x + 64 = 0. \] Step 3. Notice that the quadratic can be factored as a perfect square: \[ x^2 + 16x + 64 = (x+8)^2. \] Thus, we have: \[ (x+8)^2 = 0. \] Step 4. Solve for \( x \): \[ x + 8 = 0 \quad \Longrightarrow \quad x = -8. \] Step 5. Substitute \( x = -8 \) into the first equation to solve for \( y \): \[ y = -37(-8) - 39 = 296 - 39 = 257. \] The solution in exact form is: \[ \boxed{(-8,\,257)}. \]