Solving System Of Linear Equations

Solving System of Linear Equations The process of solving a system of equations is called solving the system The Graphing Method  Graph each equation  Find the coordinates of the point or points where all the graphs intersect (solution)  No point in common – no solution Three possibilities that can occur when two equations, each with two unknowns, are graphed  Independent and consistent  Independent and inconsistent  Dependent and consistent Practice 6.1 #13, 27, 31, 39, 49, 67 Gaussian Elimination – transform a system of equations into an equivalent system Matrix – rectangular array of numbers Augmented Matrix – a matrix containing the coefficients to a system of equations Gauss – Jordan Elimination – use row operations to produce a matrix in reduced row echelon form Row Echelon Form (450) vs. Reduced Row Echelon Form (455) Elementary Row Operations – operations performed on the rows of a systems matrix to produce row echelon form or reduced row echelon form (page 450) Examples Page 457 #14, 22, 48, 66, 74, 80 Practice 6.2 #13, 25, 31, 55, 65, 67, 71, 75