Originally Posted by

**CrashDummy11** Hey guys. Not sure this is the right sub-from, but there is not a specific section for Numerical Methods. Hopefully you guys can help me out.

"Consider wanting the roots to two equations. Specifically, your equations are:

f(x,y)=0

g(x,y)=0

In short, you want the values of {x,y}T that simultaneously render f and g equal to zero.

Question 1: Write a Taylor Series for f and g in the unknowns (truncating after the first derivative) and determine the equation(s) that must be solved to obtain the new update to your guess. In other words, derive the equation(s) that have to be solved to give you the updated estimate of the root: {xk+1,yk+1}T."