Download WARM-UP TODAY’S OBJECTIVE LINEAR SYSTEMS 3.1: SOLVING SYSTEMS

WARM-UP
Complete the below problems.
A) Find a solution to the linear equation: y  2 x  1
y  3 x  2
B) Sketch a graph of:
3.1: SOLVING SYSTEMS
USING TABLES AND
GRAPHS
TODAY’S OBJECTIVE
LINEAR SYSTEMS
• To solve a linear system using a graph or table
Systems of equations: A set of 2 or more
equations
4
X
Y1
Y2
2
-5
5
Linear system: Consists of linear equations
Solution: A set of values for all variables that
makes all the equations in the system true. Also
known as the intersection point of the lines.
-2
-4
METHOD: SOLVE BY
GRAPHING
METHOD: SOLVE BY
CREATING A TABLE
x
4
2
x  2y  4
3x  y  5
2 y   x  4
y  3 x  5
1
y  x2
2
.
5
1
y1  x  2
2
y 2  3 x  5
Y1
Y2
-2
-3
-1
-2.5
0
-2
11
8
5
1
-1.5
2
2
-1
-1
-2
-4
The lines have one intersection point. Therefore, the
solution is (2,-1)
We look for where the y-values are equal and use
those values to create the ordered pair for our
solution: (2,-1). This system is classified as
independent.
1
CLASSYIFYING SYSTEMS:
INCONSISTENT
3 x  y  4
y  2x  3
4
1
x  y 1
3
x
1
y 1
3
-5
-5
5
3 x  y  3
-2
y  3x  3
-4
When a system contains parallel lines, there is no
solution.
WRAP-UP
Consistent
Dependent –
Infinitely Many
Solutions
Systems
No Solution –
Parallel Lines
Inconsistent
6x  3y  9
3 y  6 x  9
y  2x  3
-5
-5
55
-2
-2
-4
-4
When a system contains coinciding lines, there are
infinitely many solutions.
Coach Lee offers tennis lessons at $25 per
hour. The Hunterdon Tennis Club charges $20
per hour and a registration fee of $10.
A) Write a system of equations that represents
the cost of tennis lessons in terms of hours.
B) When are the costs the same?
C) If you plan on practicing 10 hours a week,
which option is better?
TONIGHT’S HOMEWORK
APPLYING THE LESSON
c  25h
PAGES 138-139
c  20h  10
7 – 9 & 12 (Create a table), 17-27 odd, 29 – 32
x
B) 2 hours of
instruction
22
APPLYING THE LESSON
Independent –
One Solution
A)
44
6x  3y  9
2
3 x  y  4
y  3x  4
CLASSYIFYING SYSTEMS:
DEPENDENT
Y1
Y2
0
0
10
1
25
30
2
50
50
3
75
70
C) Hunterdon Tennis
Club
2