Solve the system of equations. \[ y=49 x-14 \] \( y=x^{2}+33 x+34 \) Write the coordinates in exact form. Simplify al \( (\square) \)

To solve the system of equations, we can substitute \( y \) from the first equation into the second equation: 1. Substitute \( y \): \[ 49x - 14 = x^2 + 33x + 34 \] 2. Rearranging the equation gives: \[ 0 = x^2 + 33x + 34 - 49x + 14 \] \[ 0 = x^2 - 16x + 48 \] 3. Now we can factor the quadratic: \[ 0 = (x - 12)(x - 4) \] Thus, \( x = 12 \) or \( x = 4 \). 4. Now substitute these \( x \) values back to find the corresponding \( y \): - For \( x = 12 \): \[ y = 49(12) - 14 = 588 - 14 = 574 \] So, one coordinate is \( (12, 574) \). - For \( x = 4 \): \[ y = 49(4) - 14 = 196 - 14 = 182 \] So, the other coordinate is \( (4, 182) \). The coordinates of the solutions are \( (12, 574) \) and \( (4, 182) \).