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

To solve the system of equations given by: 1. \( y = -37x - 39 \) 2. \( y = x^2 - 21x + 25 \) we can set the two expressions for \( y \) equal to each other: \[ -37x - 39 = x^2 - 21x + 25 \] Rearranging this equation gives: \[ x^2 - 21x + 25 + 37x + 39 = 0 \] Combining like terms, we get: \[ x^2 + 16x + 64 = 0 \] This quadratic can be factored as follows: \[ (x + 8)(x + 8) = 0 \] Thus, we find: \[ x + 8 = 0 \implies x = -8 \] Now, substituting \( x = -8 \) back into one of the original equations to find \( y \). We'll use the first equation: \[ y = -37(-8) - 39 = 296 - 39 = 257 \] Thus, the solution to the system of equations, in exact form, is: \[ \boxed{(-8, 257)} \]