Tools to work out the solutions in the CIS, like Cramer's rule. And we have another equation, 3x minus 2y is equal to 3. So let's say that we have an equation, 5x minus 10y is equal to 15. We're going to have to massage the equations a little bit in order to prepare them for elimination. Note: The elemental operations in rows or columns allow us to obtain equivalent systems to the initial one, but with a form that simplifies obtaining the solutions (if there are). Let's solve a few more systems of equations using elimination, but in these it won't be kind of a one-step elimination.

X = B be a system of m linear equations with n unknownįactors, m and n being natural numbers (not zero):ĪX = B is consistent independent if, and only if,.

The type of system and to obtain the solution(s), that are as: Once we have the matrix, we apply the Rouché-Capelli theorem to determine The equation system by performing elemental operations in rows (or columns). Reduced row echelon form from the augmented matrix of We apply the Gauss-Jordan Elimination method: we obtain the Obtain its echelon form or its reduced echelon

In this section we are going to solve systems using the Gaussian Elimination method, which consists in simply doing elemental operations in row or column of the augmented matrix to Is inconsistent because of we obtain the solution x = 0 from the second equation and, from the third, x = 1. Or more equations that can't be verified at the same time, If there is no solution, and this will happen if there are two If there are various solutions (the system has infinitely many solutions), we say that the system is a System is Consistent Independent System (CIS). If there is a single solution (one value for each unknown factor) we will say that the Solving a system consists in finding the value for the unknown factors in a way that verifiesĪll the equations that make up the system.

What an equation with various unknown factors does is relates them amongst each other.

Solve using elimination