Transcript 3-1 Solve Systems by Graphing

3-1
Using Graphs and Tables
to Solve Linear Systems
You will need:
-Spiral/paper to take notes
-A textbook (in this corner =>)
-The Pre-AP agreement if you
have it signed
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
A point is a solution to a system of equation if the x- and
y-values of the point satisfy both equations.
Use substitution to determine if the given
ordered pair is an element of the solution set
for the system of equations.
x – 3y = –8
(1, 3);
3x + 2y = 9
x – 3y = –8
3x + 2y = 9
(1) –3(3) –8
3(1) +2(3) 9
–8
–8 
Substitute 1 for x and 3
for y in each equation.
9
9
Because the point is a solution for both equations, it
is a solution of the system.
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Recall that you can use graphs or tables to find
some of the solutions to a linear equation. You
can do the same to find solutions to linear
systems.
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Example 2A: Solving Linear Systems by Using Graphs
and Tables
Use a graph and a table to solve the system.
Check your answer.
2x – 3y = 3
y+2=x
Solve each equation for y.
y=
x–1
y= x – 2
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Example 2A Continued
On the graph, the lines
appear to intersect at
the ordered pair (3, 1)
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
The systems of equations in Example 2 have
exactly one solution. However, linear systems
may also have infinitely many or no solutions.
A consistent system is a set of equations or
inequalities that has at least one solution, and
an inconsistent system will have no
solutions.
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
You can classify linear systems by comparing the
slopes and y-intercepts of the equations.
An independent system has equations with
different slopes. A dependent system has
equations with equal slopes and equal y-intercepts.
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Example 3A: Classifying Linear System
Classify the system and determine the number
of solutions.
x = 2y + 6
3x – 6y = 18
Solve each equation for y.
y=
x–3
y=
x–3
The equations have
the same slope and
y-intercept and are
graphed as the same
line.
The system is consistent and dependent with infinitely
many solutions.
Holt Algebra 2
3-1
Using Graphs and Tables
to Solve Linear Systems
Homework
Pg. 187-188
# 28,29,35,37,40,45
Holt Algebra 2