Solve the system of equations. \[ y=9 x+6 \] \( y=x^{2}+9 x-30 \) Write the coordinates in exact form. Simplify all fractions and radic \( (\square) \)

To solve the system of equations, we can substitute \( y \) from the first equation into the second equation: 1. Start with the equations: \[ y = 9x + 6 \] \[ y = x^2 + 9x - 30 \] 2. Set them equal to each other: \[ 9x + 6 = x^2 + 9x - 30 \] 3. Simplify by subtracting \( 9x \) from both sides: \[ 6 = x^2 - 30 \] 4. Rearranging gives us: \[ x^2 - 36 = 0 \] 5. Factoring the equation: \[ (x - 6)(x + 6) = 0 \] 6. Setting each factor to zero gives the solutions for \( x \): \[ x = 6 \quad \text{and} \quad x = -6 \] 7. Now substitute these \( x \) values back into the equation for \( y \): - For \( x = 6 \): \[ y = 9(6) + 6 = 54 + 6 = 60 \quad \Rightarrow \quad (6, 60) \] - For \( x = -6 \): \[ y = 9(-6) + 6 = -54 + 6 = -48 \quad \Rightarrow \quad (-6, -48) \] So, the coordinates in exact form are \( (6, 60) \) and \( (-6, -48) \).