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 \( x \)

Solve the system of equations \( 5x+9y=16;x+2y=4 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x+9y=16\\x+2y=4\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}5x+9y=16\\x=4-2y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\left(4-2y\right)+9y=16\) - step3: Simplify: \(20-y=16\) - step4: Move the constant to the right side: \(-y=16-20\) - step5: Subtract the numbers: \(-y=-4\) - step6: Change the signs: \(y=4\) - step7: Substitute the value of \(y:\) \(x=4-2\times 4\) - step8: Calculate: \(x=-4\) - step9: Calculate: \(\left\{ \begin{array}{l}x=-4\\y=4\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=-4\\y=4\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(-4,4\right)\) The solution to the system of equations is \( (x, y) = (-4, 4) \).