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.
$\left\{\begin{array}{ll}2 x+\lambda & =0 \\2 y+\lambda & =0 \\x+y-10 & =0\end{array}\right.$

A) x = 5 , y = -10, $\lambda$ = -10
B) x = 5, y = 5, $\lambda$ = 5
C) x = -10, y = 5, $\lambda$ = -10
D) x = 5, y = -10, $\lambda$ = 5
E) x = 5, y = 5, $\lambda$ = -10