CliffsQuickReview Algebra II
Chapter One
LINEAR EQUATIONS IN
THREE VARIABLES
Chapter Check-In
Solving systems of equations by elimination
Using matrices to solve systems of equations
Using determinants to solve equation systems
Systems of equations with three variables are only slightly more complicated
to solve than those with two variables (covered in the preceding
chapter). The two most straightforward methods of solving these
types of equations are by elimination and by using 3 x 3 matrices. Both
are treated extensively in this chapter. This chapter also explores Cramer's
rule - the application of determinant solution to equations.
Linear Equations: Solutions Using
Elimination
To use elimination to solve a system of three equations with three variables,
follow this procedure:
1. Write all the equations in standard form cleared of decimals or
fractions.
2. Choose a variable to eliminate; then choose any two of the
three equations and eliminate the chosen variable.
3. Select a different set of two equations and eliminate the same
variable as in Step 2.
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