Solve the system of equations by any method. \[ 5 x+9 y=16 \] \[ x+2 y=4 \] Enter the exact answer as an ordered pair, \( (x, y) \) If there is no solution, enter NS. If there is an infinite number of solutions, an ordered pair in terms of \( x \)

To solve the system of equations, we can use the substitution or elimination method. Here, we'll use the elimination method. Given the equations: 1. \( 5x + 9y = 16 \) 2. \( x + 2y = 4 \) First, we'll solve the second equation for \( x \): \[ x = 4 - 2y \] Now, we'll substitute \( x \) in the first equation: \[ 5(4 - 2y) + 9y = 16 \] Distributing \( 5 \): \[ 20 - 10y + 9y = 16 \] \[ 20 - y = 16 \] Now, isolate \( y \): \[ -y = 16 - 20 \] \[ -y = -4 \] \[ y = 4 \] Now, substitute \( y = 4 \) back into the expression for \( x \): \[ x = 4 - 2(4) = 4 - 8 = -4 \] Thus, the solution to the system of equations is: \[ \boxed{(-4, 4)} \]