Accurate reckoning—the entrance into the knowledge of all existing things and all obscure secrets.

Ahmes the Scribe, 17th century B.C.

sections:

  6-1, 6-2

Both chapters 6 and 7 are concerned with one topic—the efficient solution of a set of simultaneous linear equations. We will focus on those systems that have a unique solution; in particular those with n equations in n unknowns.

objectives:

• tell what is meant by a system of simultaneous linear equations
• distinguish between a system of linear equations and non-linear equations
• translate a real problem into an appropriate system of equations
• explain why a system of equations is preferred to a single equation
• solve a system of two equations by graphing
• solve a system of two equations by substitution
• solve a system of n equations by addition
• describe the possible solutions to a linear system
• show graphically the possible solutions to two equations
• write out the elementary equation operations to produce equivalent systems
• use the elementary equation operations to solve a system
• write out the matrix of coefficients for a system of equations
• produce the augmented matrix
• write out the elementary row operation to produce a equivalent matrix
• identify the transformed matrix that gives the solution
• use the elementary row operations to solve a matrix
• solve a system of equations by the Gauss-Jordan Elimination
• during the solution process, identify when a system does not have a unique solution