Download 3-1 Using Graphs and Tables to Solve Linear Systems

3-1
Using Graphs and Tables to Solve Linear Systems
Warm Up
Write each equation in slope-intercept form.
1. 2y + 8x = 6
2. 4y – 3x = 8
3-1
Using Graphs and Tables to Solve Linear Systems
LEARNING GOALS FOR LESSON 3.1
1. Verify a point is a solution to a
system
2. Solve a system using a graph and a
table
3. Classify the number of solutions
3-1
Using Graphs and Tables to Solve Linear Systems
A System of Equations is a set of two or more equations containing
two or more variables.
•  On the graph of the system of two equations, the Solution is the
set of points where the lines intersect.
3-1
Using Graphs and Tables to Solve Linear Systems
Example 1: Verifying Solutions of Linear Systems
Use substitution to determine if the given ordered pair is an
element of the solution set for the system of equations.
# x − 3y = −8
# x + 6 = 4y
1
A. 1 ,3 ; $
B. −4 , 2 ; $
%3x + 2y = 9
%2x + 8y = −4
(
(
)
€
)
3-1
Using Graphs and Tables to Solve Linear Systems
Example 2: Solving Linear Systems by Using Graphs and Tables
Use a graph to solve the system. Check your answer with a
table.
Step 1: Solve each equation for y = mx + b
# y = −2x + 1
$
Step 2: Graph each equation.
%y + 2 = x
Step 3: Plug in points with x-values around the
intersection point’s x-value to each equation to
determine the final answer.
Step 4: Write the SOLUTION: ( _____, _____)
Equation 1
x y=
Equation 2
x y=
3-1
Using Graphs and Tables to Solve Linear Systems
Example 2: Solving Linear Systems by Using Graphs and Tables
Use a graph to solve the system. Check your answer with a
table.
# y = −2x + 1
$
%y + 2 = x
Equation 1
x y
Equation 2
x y
3-1
Using Graphs and Tables to Solve Linear Systems
Example 2: Solving Linear Systems by Using Graphs and Tables
Use a graph and a table to solve the system. Check your
answer.
Step 1: Solve each equation for y = mx + b
#x − y = 2
%
A. $
3
1
y
=
x
−
%
&
2
2
Step 2: Graph each equation in the calculator.
1. Push Y=
2. Type in the 1st equation into Y1 and the 2nd equation into Y2.
3. Push GRAPH
4. If you have trouble seeing the graph push ZOOM and choose option
0: ZoomFit or 6:ZStandard
Step 3: Pull up the table on your calculator.
1. Push 2nd and then GRAPH.
2. Scroll to where you think the intersection point is.
OR
Step 3: Find the intersection point from the graph.
1. Push 2nd and then TRACE then choose option 5: intersect.
2. Press ENTER 3 times and it will give you the intersection point.
Step 4: Write the SOLUTION: ( _____, _____)
3-1
Using Graphs and Tables to Solve Linear Systems
Example 2: Solving Linear Systems by Using Graphs and Tables
Use a graph and a table to solve the system. Check your
answer.
#x − y = 2
%
A. $
3
1
y
=
x
−
%
&
2
2
#2y + 6 = x
B. $
% y = 4x − 3
€
3-1
Using Graphs and Tables to Solve Linear Systems
Consistent/
Inconsistent
Dependent/
Independent
Exactly One
Solution
Infinitely Many
Solutions
No Solutions
Consistent and
Independent
Consistent and
Dependent
Inconsistent
Are NOT =
Can be = or NOT =
Are =
Are =
Are =
Are NOT =
Looks Like
Slopes
y-intercepts
3-1
Using Graphs and Tables to Solve Linear Systems
Example 3: Classifying Linear System
Classify the system and determine the number of solutions.
#x − y = 2
A. %
$
3
1
%y = x −
&
2
2
B.
€
#
1
y
=
x −3
%
%
2
$
%y = 1 x − 2
%
&
2
"2 y = x − 4
$
1
C. #
y=
x−2
$
%
2