Chapter 1.3, Problem 35E

Calculus In Exercises $35$ and $36,$ find the values of $x,y,$ and $\lambda$ that satisfy the system of equations. Such systems arise in certain problems of calculus, and $\lambda$ is called the Lagrange multiplier.

$\begin{array}{l}2x+\lambda =0\\ 2y+\lambda =0\\ x+y-4=0\end{array}$