What is the solution to this system of equations? \( \begin{array}{l}y=2-x \\ 3 x-2 y=16 \\ (4,-2) \\ (0,2) \\ (5,-3) \\ (-4,2)\end{array} \)

To solve the system of equations, we can substitute the first equation \( y = 2 - x \) into the second equation \( 3x - 2y = 16 \). Substituting gives: \[ 3x - 2(2 - x) = 16 \\ 3x - 4 + 2x = 16 \\ 5x - 4 = 16 \\ 5x = 20 \\ x = 4 \] Now, substituting \( x = 4 \) back into \( y = 2 - x \): \[ y = 2 - 4 = -2 \] Thus, the solution to the system of equations is \( (4, -2) \). Now, let’s analyze the potential solutions provided: 1. **(4, -2)** is our correct solution. 2. **(0, 2)**: If we plug these values into the second equation, we find \( 3(0) - 2(2) = -4 \), which does not equal 16. 3. **(5, -3)**: Checking this in the second equation gives \( 3(5) - 2(-3) = 15 + 6 = 21 \), which is also incorrect. 4. **(-4, 2)**: Finally, substituting gives \( 3(-4) - 2(2) = -12 - 4 = -16 \), another miss. Thus, the only valid point from the options is \( (4, -2) \).