Equation Solving
A few examples of what you can ask Wolfram|Alpha about:
solve a linear equation
solve a polynomial equation
solve over a spcified domain
solve an equation with parameters
solve a trigonometric equation
Systems of Equations
solve a system of linear equations
solve a system of polynomial equations
find roots of an equation using Newton's method
find roots of an equation using the secant method
compute the nth root of a number using the bisection method