Chapter 2: Systems of Linear
Equations and Inequalities
This chapter reviews the concepts of
solving systems of linear equations and
inequalities and operations with
matrices.
Section 2-1: Solving systems of
equations in two variables
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A system of equations is a set of two or more
equations. To “solve” a system of equations
means to find values for the variables in the
equations which make ALL the equations
true.
You can solve a system by graphing and
finding the intersection of the graphs (points
common to all equations). These points are
the solutions of the system of equations.
Vocabulary
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A consistent system of equations has at least
one solution.
If there is exactly one solution, the system is
independent.
If there are infinitely many solutions, the
system is dependent.
If there is no solution, the system is
inconsistent.
Characteristics of these types of
systems
Consistent
Independent
Different slope
Inconsistent
Dependent
Same slope
Same intersect
Lines intersect
Graphs are
same line
One solution
Infinitely many
solutions
Same slope
Different intercepts
Lines are parallel
No solution
Solving a system of linear equations
algebraically
The elimination method Example 5x+2y=340
3x-4y=360
Multiple the first equation by 2
10x+4y=680
3x-4y=360
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Add
13x=1040
x=80
Now substitute in to either equation x=80 and solve for y. Y=-30
So the solution to this system is (80,-30). Plugging it into both
equations, makes both equations true.
The Substitution Method
Another method to solve a system of linear equations algebraically
is using the substitution method.
„ Example: y=3x-8
2x+y=22
Substitute the first equation into the second equation and solve for x.
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2x+ 3x-8=22
5x-8=22
5x=30
x=6
Now plug x=6 into either equation and solve for y. Y=10. Therefore the
solution to this system of equations is (6,10). That means this
ordered pair makes both equations true.
HW #10
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Section 2-1
Pp 71-72
#11-15 all,17,21,23,33