Lagrange Multiplier Maximization Problem

This is an example problem our professor gave us but after getting the partials, it jumps right to the answer for x and y. Is solving this problem just a matter of doing some algebra to solve for x and y using the three resulting equations from the partial derivatives?

Maximize 2x-5y subject to x^4 + y^4 = 1

F(x,y,L) = 2x-5y+L(x^4+y^4-1)

partial of F with respect to x, 2+4*L*x^3=0

partial of F with respect to y, -5+4*L*y^3=0

partial of F with respect to L, x^4 + y^4 -1=0