Find Values of X, Y, And $\lambda$ That Satisfy the System $\lambda$

Multiple Choice

Find values of x, y, and $\lambda$ that satisfy the system.These systems arise in certain optimization problems in calculus, and $\lambda$ is called a Lagrange multiplier.
$$\left\{ \begin{array} { l } 2 + 2 y + 2 \lambda = 0 \\2 x + 1 + \lambda = 0 \\2 x + y - 96 = 0\end{array} \right.$$

A) x = 24, y = -49, $\lambda$ = 24
B) x = -49, y = 48, $\lambda$ = -49
C) x = 24, y = 48, $\lambda$ = -49
D) x = 24, y = -49, $\lambda$ = -49
E) x = 24, y = 48, $\lambda$ = 48