**GNU Emacs Calc 2.02 Manual**

### 11.7.3 Systems of Equations

The `a R` command can also solve systems of equations. In this
case, the equation should instead be a vector of equations, the
guess should instead be a vector of numbers (intervals are not
supported), and the variable should be a vector of variables. You
can omit the brackets while entering the list of variables. Each
equation must be differentiable by each variable for this mode to
work. The result will be a vector of two vectors: The variable
values that solved the system of equations, and the differences
between the sides of the equations with those variable values.
There must be the same number of equations as variables. Since
only plain numbers are allowed as guesses, the Hyperbolic flag has
no effect when solving a system of equations.

It is also possible to minimize over many variables with `a N`
(or maximize with `a X`). Once again the variable name should
be replaced by a vector of variables, and the initial guess should
be an equal-sized vector of initial guesses. But, unlike the case of
multidimensional `a R`, the formula being minimized should
still be a single formula, *not* a vector. Beware that
multidimensional minimization is currently *very* slow.