1. The problem statement, all variables and given/known data Find the shortest distance from the origin to the surface x=yz+10 2. Relevant equations 3. The attempt at a solution So I said that my main function, f(x,y,z) = x^2 + y^2 + z^2 (the function I want to minimize) Then I said that g(x,y,z) is my constraint function where g(x,y,z) is yz-x=-10. I took the partial derivative with respect to each variable of both g and f. I got fx=2x, fy=2y, fz=2z, gx=-1, gy=z, and gz=y. Once I did this, set fx = λ gx etc. (same format for each partial). This is where I am confused. My final equations are: 2x + λ = 0 (1) 2y - λz = 0 (2) 2z - λy = 0 (3) yz - x = 10 (4) Once I have these, I am confused as to how to solve them properly. What I did so far was solve equation 2 for z. Once I solved for z in terms of y and λ, I substituted it back in to equation 3 and got 4y/λ - λy = 0. Multiplying lambda across, I get 4y = λ2y. This shows me that either λ=2 or y=0. Once I get these, for each case I solved and when y = 0, plugging back in to equation 2, I get z = 0, and this means that x=10 (equation 4). However, if λ = 2, then by equation 1, x=-1. My question is: What should I be looking for here? What do I solve for to answer the question properly?