Give two solutions to the equation \( y=\sqrt{10-x} \). Give your solutions as ordered pairs, using exact values (integers or radicals) coordinates.

To find the solutions to the equation \( y = \sqrt{10 - x} \), we need to solve for \( x \) in terms of \( y \). However, since the equation involves a square root, we will have to consider two cases: one where the square root is non-negative, and one where it is negative. The square root of a negative number is not a real number, so we will only consider the non-negative case. Here are the steps to solve for \( x \): 1. Square both sides of the equation to eliminate the square root: \[ y^2 = (\sqrt{10 - x})^2 \] \[ y^2 = 10 - x \] 2. Rearrange the equation to solve for \( x \): \[ x = 10 - y^2 \] Now, we can find the ordered pairs by substituting different values of \( y \) into the equation \( x = 10 - y^2 \). Since we are looking for exact values, we will use integers or radicals for \( y \). Solution 1: Let's choose \( y = 0 \): \[ x = 10 - 0^2 \] \[ x = 10 \] So, the first ordered pair is \( (10, 0) \). Solution 2: Let's choose \( y = 3 \) (since \( 3^2 = 9 \) is a perfect square and will give us a real value for \( x \)): \[ x = 10 - 3^2 \] \[ x = 10 - 9 \] \[ x = 1 \] So, the second ordered pair is \( (1, 3) \). Therefore, the two solutions to the equation \( y = \sqrt{10 - x} \) as ordered pairs with exact values are \( (10, 0) \) and \( (1, 3) \).