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

question 273

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

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