Download infinitely many solutions

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Copy HW in your planner.
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Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36
Be ready to finish quiz sections 7.1 – 7.4. You
will have 10 minutes.
Objective
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SWBAT identify the number of solutions of a
linear system
“How Do You Solve a Linear System???”
(1) Solve Linear Systems by Graphing (7.1)
(2) Solve Linear Systems by Substitution (7.2)
(3) Solve Linear Systems by ELIMINATION!!! (7.3)
Adding or Subtracting
(4) Solve Linear Systems by Multiplying First (7.4)
Then eliminate.
Section 7.5 “Solve Special Types of Linear
Systems”
LINEAR SYSTEMconsists of two or more linear equations in the same
variables.
Types of solutions:
(1) a single point of intersection – intersecting lines
(2) no solution – parallel lines
(3) infinitely many solutions – when two equations
represent the same line
“Solve Linear Systems by Elimination”
Multiplying First!!”
Equation 1
4x + 5y = 35
x (2)
Equation 2
-3x + 2y = -9
x (-5)
“Consistent Independent
System”
4x + 5y = 35 Equation 1
4(5) + 5y = 35
20 + 5y = 35
y=3
4(5) + 5(3) = 35
35 = 35
+
8x + 10y = 70
15x - 10y = 45
23x
= 115
x=5
Substitute value for
x into either of the
original equations
The solution is the point (5,3).
Substitute (5,3) into both
equations to check.
-3(5) + 2(3) = -9
-9 = -9
“Solve Linear Systems with No Solution”
Equation 1
Equation 2
_
+
“Inconsistent
System”
3x + 2y = 10
-3x
3x + (-2y)
2y = =2 -2
0=8
This is a false statement,
therefore the system has no
solution.
No Solution
By looking at the graph, the lines
are PARALLEL and therefore will
never intersect.
“Solve Linear Systems with Infinitely Many Solutions”
Equation 1
“Consistent
Dependent
System”
Equation 1
x – 2y = -4
Equation 2
y = ½x + 2
x – 2(½x
2y = -4
+ 2) = -4
x – x – 4 = -4
Use ‘Substitution’
because we know
what y is equals.
This is a true statement,
therefore the system has
infinitely many solutions.
-4 = -4
Infinitely Many Solutions
By looking at the graph, the
lines are the SAME and
therefore intersect at every
point, INFINITELY!
“Tell Whether the System has No Solutions or
Infinitely Many Solutions”
Equation 1
Equation 2
+
“Inconsistent
System”
5x + 3y = 6
-5x - 3y = 3
This is a false statement,
therefore the system has no
solution.
0=9
No Solution
“Tell Whether the System has No Solutions or
Infinitely Many Solutions”
Equation 1 -6x + 3y = -12
Equation 2
Equation 1
“Consistent
Dependent
System”
y = 2x – 4
-6x + 3(2x
3y = -12
– 4) = -12
-6x + 6x – 12 = -12
Use ‘Substitution’
because we know
what y is equals.
This is a true statement,
therefore the system has
infinitely many solutions.
-12 = -12
Infinitely Many Solutions
How Do You Determine the Number of
Solutions of a Linear System?
(1)First rewrite the equations in slope-intercept form.
(2)Then compare the slope and y-intercepts.
slope
y -intercept
y = mx + b
Number of Solutions
Slopes and y-intercepts
One solution
Different slopes
No solution
Same slope
Different y-intercepts
Same slope
Same y-intercept
Infinitely many solutions
“Identify the Number of Solutions”
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Without solving the linear system, tell whether
the system has one solution, no solution, or infinitely
many solutions.
5x + y = -2
-10x – 2y = 4
6x + 2y = 3
6x + 2y = -5
Infinitely many
solutions
No solution
y = -5x – 2
– 2y =10x + 4
y = -5x – 2
y = 3x + 3/2
y = 3x – 5/2
3x + y = -9
3x + 6y = -12
One solution
y = -3x – 9
y = -½x – 2
WAR!!
“Identify the Number of Solutions”
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Without solving the linear system, tell whether
the system has one solution, no solution, or infinitely
many solutions.
NJASK7 Prep
Homework
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Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36