the best method for solving system of equation

Question

What is the best method for solving systems of equations? Is there an advantage of one method versus another? Also, discuss how you can reduce rational expression to lowest term. Justify with examples.

Answer 1

Best: substitution, especially on 2 by 2 systems.

Worst: graphing, because accuracy of intersecting lines is limited.

Good: Cramer's rule using determinants, practical & feasible in systems of 2 or 3 equations.

Easy: RREF operation on Augmented matrix representing the system, on a graphing calculator such as TI-84.

Formal & somewhat tedious, in my opinion: Using Matrix inversion to solve AX = B by X = A^-1B.

Tedious & error prone: manual Gauss-Jordan "row operations" on the augmented matrix representation of the system.

 

Always check the answers!  Don't forget the technique of Clearing fractions, to eliminate all fractional coefficients.