Page 180 - Math Course 2 (Book 1)

Systems of Equations

MO. 6 - L1b y

Solving Systems of Equations

by Graphing 2x – y = –3

0 x
Key Concept

Graphing Systems of 8x – 4y = –12
Equations

Graph of a Number of Terminology The graphs coincide. There are
System Solutions Answer inf nitely many solutions of this
system of equations.
y
Graph the system of equations. Then determine
Exactly one Consistent whether the system has no solution, one solution,
solution and
0 x or inf nitely many solutions. If the system has one
Independent
solution, name it.
x – 2y = 4
x – 2y = –2
y
y
Inf nitely Consistent x – 2y = –2
0 x many and
dependent

0 x

y
x – 2y = 4
No solutions Inconsistent
0
x The graphs are parallel lines.
Since they do not intersect, there
Answer
are no solutions of this system of
equations.

Let’s Begin Write and Solve a System of
Equations

Examples
Solve a System of Equations

Examples BICYCLING
Tyler and Pearl went on a 20-kilometer
bike ride that lasted 3 hours. Because of
the steep hills on the ride, they had to walk
Graph the system of equations. Then determine for most of the trip. Their walking speed was 4
whether the system has no solution, one solution, kilometers per hour.
or inf nitely many solutions. If the system has one
solution, name it. Their riding speed was 12 kilometers per hour.
2x – y = –38 How much time did they spend walking?
8x – 4y = –12

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