Find the values of x y and A that satisfy the system of equa

Find the values of x, y, and A that satisfy the system of equations. Such systems arise in certain problems of calculus, and A is called the Lagrange multiplier. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

Solution

Answer :

From the first equation , 3x = - so that x = - /3

From the second equation 3y = - so that y = - /3

That is x = y = - /3

From the third equation x + y = 4 => 2x = 4 or x = 2 and then y = 2 , = - 6

Thus the values of x , y and that the system satisfies are ( x , y , ) = ( 2 , 2 , - 6 )