Hey there,

if don't want to self-implement a Newton scheme, there's a built-in rountine available: fsolve() that solves F(x) = 0. Assuming your two equations are scalar, use something like

F = @(x) [x(1)^2 - 3*cos(x(2)) - a; 2*x(1) + x(2)^3 + b];

x0 = [1;1];

xroot = fsolve(F, x0);

Verify the solution by typing F(xroot) (which should be close to the zero vector). This works analogously for vector-valued equations.

Best, FF