selve the system of equations. \[ y=x^{2}+3 x-48 \] \( y=3 x+96 \) White the coordinates in exact form. Simplify all fractions and radic \( ( \), \( ) \)

To solve the system of equations, we start by substituting \( y \) from the second equation into the first: \[ 3x + 96 = x^2 + 3x - 48 \] Now, we can simplify this: \[ 3x + 96 - 3x = x^2 - 48 \] \[ 96 = x^2 - 48 \] \[ x^2 - 48 - 96 = 0 \] \[ x^2 - 144 = 0 \] Now, factor the equation: \[ (x - 12)(x + 12) = 0 \] Thus, \( x = 12 \) or \( x = -12 \). Now substitute these \( x \) values back into the second equation to find the corresponding \( y \) values. 1. For \( x = 12 \): \[ y = 3(12) + 96 = 36 + 96 = 132 \] 2. For \( x = -12 \): \[ y = 3(-12) + 96 = -36 + 96 = 60 \] Therefore, the coordinates in exact form are \( (12, 132) \) and \( (-12, 60) \).