Solve the system of equations. \[ \begin{array}{l}y=50 x^{2}-18 x-36 \\ y=-18 x+14\end{array} \] Write the coordinates in exact form. Simplify all fractions and radica ( ,

To solve the system of equations, we will set the two equations equal to each other since both equal \(y\): \[ 50x^2 - 18x - 36 = -18x + 14 \] Now, simplify it: \[ 50x^2 - 36 = 14 \] Adding 36 to both sides gives: \[ 50x^2 = 50 \] Dividing both sides by 50 results in: \[ x^2 = 1 \] Taking the square root of both sides, we find: \[ x = 1 \quad \text{or} \quad x = -1 \] Now, we'll substitute these values back into the second equation \(y = -18x + 14\) to find the corresponding \(y\) values. For \(x = 1\): \[ y = -18(1) + 14 = -18 + 14 = -4 \] For \(x = -1\): \[ y = -18(-1) + 14 = 18 + 14 = 32 \] Thus, the solutions to the system of equations are: \[ (1, -4) \quad \text{and} \quad (-1, 32) \] So, the coordinates in exact form are \((1, -4)\) and \((-1, 32)\).