Find Values of X, Y, and λ That Satisfy the System

Short Answer

Find values of x, y, and λ that satisfy the system. These systems arise in certain optimization problems in calculus, and λ is called a Lagrange multiplier.
​ $$\left\{ \begin{array} { r } 4 x - 4 x \lambda = 0 \\- 2 y + \lambda = 0 \\y - x ^ { 2 } = 0\end{array} \right.$$ ​