Page 178 - Math Course 2 (Book 1)

Systems of Equations

Mo. 6

Lesson 1 independent
If a consistent system has exactly one solution, it is
independent.
KEY CONCEPTS:
1. Determine whether a system of linear
equations has no, one, or inf nitely many
solutions.
2. Solve systems of equations by graphing.

MO. 6 - L1a
Intersecting Lines
Solutions of Systems of Exactly one solutions
Equations dependent

Vocabulary A-Z If a consistent system has inf nite solutions, it is
dependent.
Let us learn some vocabulary

system of equations
Two or more equations containing common
variables. Linear equations (or linear system) are
a collection of linear equations involving the same
set of variables.

The following 3 equations involve the same Same Lines
variables: x, y and z. Inf nitely many Solutions

3x + 2y – z = 1 inconsistent

2x – 2y + 4z = –2 A system of equations which has no solutions. If
1 the graphs are parallel, the system of equations is
–x + y – z = 0
2 said to be inconsistent. There are no solutions.
consistent
y
A system of equations that has at least one
solution. If the graphs intersect or coincide, the
system of equations is consistent. It has at least
one ordered pair that satisf es both equations.
0
y x

Attempts to solve inconsistent systems typically
results in impossible or untrue statements such
0 as 0 = 3.
x

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