Algebra II Essentials For Dummies

Chapter 11

Solving Systems of Equations

IN THIS CHAPTER

Finding solutions for systems of two, three, or more linear equations

Determining if and where lines and parabolas intersect

Expanding the search for intersections to other curves

A system of equations consists of a number of equations with common variables — variables that are linked in a specific way. The solution of a system of equations consists of the sets of numbers that make each equation in the system a true statement or a list of relationships between numbers that makes each equation in the system a true statement.

In this chapter, I cover both systems of linear equations and some nonlinear equations. You have a number of techniques at your disposal to solve systems of equations, including graphing lines, adding multiples of one equation to another, and substituting one equation into another.

Looking at Solutions Using the Standard Linear-Systems Form

The standard form for a system of linear equations is as follows:

The x’s all represent variables, the k’s are constants, and the a, b, c, and so on all represent constant ...