Solve the system of equations. \[ \begin{array}{l}y=x^{2}-29 x-49 \\ y=-29 x+72\end{array} \] Write the coordinates in exact form. Simplify all fractions and ra

To solve the system of equations, we can set the two equations equal to each other since both equal \(y\): \[ x^{2} - 29x - 49 = -29x + 72 \] Now we can simplify this by adding \(29x\) to both sides: \[ x^{2} - 49 = 72 \] Next, add \(49\) to both sides: \[ x^{2} = 121 \] Taking the square root of both sides, we find: \[ x = 11 \quad \text{or} \quad x = -11 \] Now, we'll substitute these values of \(x\) back into one of the original equations to find the corresponding \(y\) values. Let's use the second equation \(y = -29x + 72\). 1. For \(x = 11\): \[ y = -29(11) + 72 = -319 + 72 = -247 \] So one solution is \((11, -247)\). 2. For \(x = -11\): \[ y = -29(-11) + 72 = 319 + 72 = 391 \] So the second solution is \((-11, 391)\). Thus, the coordinates in exact form are: \[ (11, -247) \quad \text{and} \quad (-11, 391) \]