Chapter 8
SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
The four preceding chapters investigate, in some depth, the solutions
and graphs of linear equations and inequalities in one and two variables.
Though the concepts and techniques vary widely, one universal characteris-
tic unites them: each considers only one equality or inequality statement at
a time. This chapter introduces systems, the solutions of which satisfy mul-
tiple statements rather than single equations or inequalities.
A system of equations is a group of (usually two) equations. Your goal
is to nd one x-value and one y-value that make BOTH of the equations
true when you substitute them in. That means the solution of a system
of equations is usually a point (x,y). There are a few special cases when
there’s no answer or more than one answer, and you’ll deal with those as
well.
Remember the graphs of inequalities from the end of Chapter 7?
They were shaded regions in the coordinate plane. This chapter deals
with systems of inequalities, multiple inequalities on the same graph,
which means even more shading. The last thing you deal with is linear
programming, which is a “real life” application of systems of inequalities.
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