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.
$\left\{\begin{array}{ll}
y+\lambda & =0 \
x+\lambda & =0 \
x+y-18 & =0
\end{array}\right.$
A) x = 9, y = 9, $\lambda$ = -9
B) x = 9, y = -9, $\lambda$ = -9
C) x = 9, y = -9, $\lambda$ = 9
D) x = 9, y = 9, $\lambda$ = 9
E) x = -9, y = 9, $\lambda$= -9

Question

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.
 $\left\{\begin{array}{ll}
y+\lambda & =0 \
x+\lambda & =0 \
x+y-18 & =0
\end{array}\right.$  
A) x = 9, y = 9, $\lambda$ = -9
B) x = 9, y = -9, $\lambda$ = -9
C) x = 9, y = -9, $\lambda$ = 9
D) x = 9, y = 9, $\lambda$ = 9
E) x = -9, y = 9, $\lambda$= -9

Quizplus · Accepted Answer

From the first two equations, $y + \lambda = 0$ and $x + \lambda = 0$, we can see that $x = y$. Substituting $x = y$ into the third equation, $x + y - 18 = 0$, gives $2x = 18$, so $x = 9$, and therefore $y = 9$. Substituting $x = 9$ into $x + \lambda = 0$ gives $\lambda = -9$.

Find Values of X, Y, And λ\lambdaλ That Satisfy the System λ\lambdaλ

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