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**holly123** find the maximum and minimum values of the function subject to the given contraint.

f(x,y)= 8x+3y

subject to (x-1)^2 + (y+2)^2 = 9

so i took the gradient of each..

(8, 3)

(2x-2, 2y+2)

and to solve for the max and min, we need to use lagrange multipliers. so the gradient of f is equal to the gradient of g times lambda (some constant)

i have the equations

8= lambda(2x-2)

3=lambda(2y+4)

(x-1)^2 + (y+2)^2 =9

how do i solve this system of equations? the answer in the back of the book is kind of crazy...

x= 1 - 24/sqrt 73

y= -2- 9/sqrt 73

lambda= -sqrt 73/6