Cramer's Rule can be used to solve a system of linear equations:
Given a system of linear equations A*x=b where A is an invertible square matrix, the theorem says that $ <img class="tex" alt=" x_i = \frac{\det(A_i)}{\det(A)} \qquad i = 1, \ldots, n \, " src="http://upload.wikimedia.org/math/f/7/7/f772877984cbae5c47877d4ced245b6c.png"> $, where Ai is a matrix formed by replacing the ith column of A with the vector b.
