Determine whether each ordered pair is a solution of the given linear equation.
\[
2 x+5 y=16 ;(3,2),(9,0),(0,4)
\]
Is $(3,2)$ a solution to the given linear equation?
No
Yes
Is $(9,0)$ a solution to the given linear equation?
Yes
No
Is $(0,4)$ a solution to the given linear equation?
Yes
No

Step 1 ：Plug in the x and y values of each ordered pair into the equation \(2x + 5y = 16\) and check if the equation holds true.

Step 2 ：Check if \((3,2)\) is a solution: \(2(3) + 5(2) = 6 + 10 = 16\). Since the equation holds true, \((3,2)\) is a solution.

Step 3 ：Check if \((9,0)\) is a solution: \(2(9) + 5(0) = 18 + 0 = 18\). Since the equation does not hold true, \((9,0)\) is not a solution.

Step 4 ：Check if \((0,4)\) is a solution: \(2(0) + 5(4) = 0 + 20 = 20\). Since the equation does not hold true, \((0,4)\) is not a solution.

Step 5 ：\(\boxed{\text{Final Answer:}}\)

Step 6 ：\(\boxed{(3,2)\text{ is a solution to the given linear equation.}}\)

Step 7 ：\(\boxed{(9,0)\text{ is not a solution to the given linear equation.}}\)

Step 8 ：\(\boxed{(0,4)\text{ is not a solution to the given linear equation.}}\)