Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12,...
-
Upload
edith-newton -
Category
Documents
-
view
213 -
download
1
Transcript of Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12,...
Do Now 1/15/10Do Now 1/15/10
Copy HW in your planner.Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 Text p. 462, #1-8 all, #10, #12, #16-30
evens, #36evens, #36
Be ready to finish quiz sections 7.1 – Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes.7.4. You will have 10 minutes.
ObjectiveObjective
SWBAT identify the number of SWBAT identify the number of solutions of a linear systemsolutions of a linear system
““How Do You Solve a Linear How Do You Solve a Linear System???”System???”
(1) (1) Solve Linear Systems by Graphing (7.1)Solve Linear Systems by Graphing (7.1)
(2) (2) Solve Linear Systems by Substitution (7.2)Solve Linear Systems by Substitution (7.2)
(3) Solve Linear Systems by (3) Solve Linear Systems by ELIMINATION!!!ELIMINATION!!! (7.3)(7.3)
Adding or SubtractingAdding or Subtracting
(4) (4) Solve Linear Systems by Multiplying FirstSolve Linear Systems by Multiplying First (7.4) (7.4)
Then eliminate.Then eliminate.
Section 7.5 “Solve Special Types of Section 7.5 “Solve Special Types of Linear Systems”Linear Systems”
LINEAR SYSTEM-LINEAR SYSTEM-consists of two or more linear equations consists of two or more linear equations
in the same variables.in the same variables.
Types of solutions:Types of solutions:(1) (1) a a single pointsingle point of intersection of intersection – – intersecting linesintersecting lines
(2) (2) no solutionno solution – parallel lines – parallel lines
(3) (3) infinitely many solutionsinfinitely many solutions – when two – when two equations represent the same lineequations represent the same line
Equation 1 Equation 1
-3x + 2y = -9-3x + 2y = -9 Equation 2Equation 2
4x + 5y = 35 4x + 5y = 35
““Solve Linear Systems by Elimination” Solve Linear Systems by Elimination” Multiplying First!!” Multiplying First!!”
Equation 1 Equation 1 4x + 5y = 354x + 5y = 35 Substitute value forSubstitute value forx into either of the x into either of the original equations original equations 4(5) + 5y = 354(5) + 5y = 35
20 + 5y = 3520 + 5y = 35
The solution is the point (5,3). The solution is the point (5,3). Substitute (5,3) into both Substitute (5,3) into both
equations to check.equations to check.
4(5) + 5(3) = 354(5) + 5(3) = 3535 = 3535 = 35
-3(5) + 2(3) = -9-3(5) + 2(3) = -9-9 = -9-9 = -9
Multiply Multiply
FirstFirst
++ 23x = 11523x = 115
x = 5x = 5
y = 3y = 3
EliminatedEliminated
x (2)x (2)
15x - 10y = 4515x - 10y = 45 8x + 10y = 70 8x + 10y = 70
x (-5)x (-5)
““Consistent IndependentConsistent IndependentSystem”System”
Equation 1 Equation 1
3x + 2y = 2 3x + 2y = 2 Equation 2Equation 2
3x + 2y = 10 3x + 2y = 10
““Solve Linear Systems with No Solve Linear Systems with No Solution”Solution”
_
0 = 80 = 8
No SolutionNo Solution
EliminatedEliminated EliminatedEliminated
-3x + (-2y) = -2 -3x + (-2y) = -2 +This is a false statement,therefore the system has nosolution.
By looking at the graph, the lines are PARALLEL and therefore willnever intersect.
“ “InconsistentInconsistentSystem”System”
Equation 1 Equation 1
Equation 2Equation 2
x – 2y = -4 x – 2y = -4
““Solve Linear Systems with Infinitely Many Solve Linear Systems with Infinitely Many Solutions”Solutions”
-4 = -4-4 = -4
Infinitely Many SolutionsInfinitely Many Solutions
y = ½x + 2 y = ½x + 2
This is a true statement,therefore the system has infinitely many solutions.
By looking at the By looking at the graph, the lines are the graph, the lines are the SAME and therefore SAME and therefore intersect at every point, intersect at every point, INFINITELY!INFINITELY!
“ “ConsistentConsistentDependentDependent
System”System”
Equation 1 Equation 1 x – 2y = -4x – 2y = -4
Use ‘Substitution’ Use ‘Substitution’ because we know because we know what y is equals.what y is equals.
x – x – 4 = -4x – x – 4 = -4 x – x – 22(½x + 2)(½x + 2) = -4 = -4
Equation 1 Equation 1
Equation 2Equation 2
5x + 3y = 6 5x + 3y = 6
““Tell Whether the System has NTell Whether the System has No o SolutionsSolutions or or Infinitely Many Infinitely Many
SolutionsSolutions””
+
0 = 90 = 9
No SolutionNo Solution
EliminatedEliminated EliminatedEliminated
-5x - 3y = 3 -5x - 3y = 3 This is a false statement,therefore the system has nosolution.
“ “InconsistentInconsistentSystem”System”
Equation 1 Equation 1
Equation 2Equation 2
-6x + 3y = -12 -6x + 3y = -12
-12 = -12-12 = -12
Infinitely Many SolutionsInfinitely Many Solutions
y = 2x – 4 y = 2x – 4
This is a true statement,therefore the system has infinitely many solutions.
“ “ConsistentConsistentDependentDependent
System”System”
Equation 1 Equation 1 -6x + 3y = -12-6x + 3y = -12
Use ‘Substitution’ Use ‘Substitution’ because we know because we know what y is equals.what y is equals.
-6x + 6x – 12 = -12-6x + 6x – 12 = -12 -6x + 3-6x + 3(2x – 4)(2x – 4) = -12 = -12
““Tell Whether the System has NTell Whether the System has No o SolutionsSolutions or or Infinitely Many Infinitely Many
SolutionsSolutions””
How Do You Determine the How Do You Determine the Number of Solutions of a Number of Solutions of a
Linear System?Linear System?
Number of Number of SolutionsSolutions
Slopes and y-Slopes and y-interceptsintercepts
One solutionOne solution Different slopesDifferent slopes
No solutionNo solution Same slope Same slope
Different y-interceptsDifferent y-intercepts
Infinitely many Infinitely many solutionssolutions
Same slope Same slope
Same y-interceptSame y-intercept
(1)First rewrite the equations in slope-intercept form. (2)Then compare the slope and y-intercepts.
y = mx + by = mx + bslope y -intercept
““Identify the Number of Identify the Number of Solutions”Solutions”
Without solving the linear system, Without solving the linear system, tell whether the system has tell whether the system has one one solution, no solution, solution, no solution, or or infinitely infinitely many solutions.many solutions. 5x + y = -25x + y = -2
-10x – 2y = 4-10x – 2y = 46x + 2y = 36x + 2y = 3
6x + 2y = -56x + 2y = -5
Infinitely many Infinitely many solutionssolutions
No solutionNo solution
3x + y = -93x + y = -9
3x + 6y = -123x + 6y = -12
One solutionOne solution
y = -5x – 2y = -5x – 2
– – 2y =10x + 42y =10x + 4
y = -5x – 2y = -5x – 2
y = 3x + 3/2 y = 3x + 3/2
y = 3x – 5/2y = 3x – 5/2y = -3x – 9y = -3x – 9
y = -½x – 2 y = -½x – 2
WAR!!WAR!!“Identify the Number of “Identify the Number of
Solutions”Solutions” Without solving the linear system, Without solving the linear system,
tell whether the system has tell whether the system has one one solution, no solution, solution, no solution, or or infinitely infinitely many solutions.many solutions.
HomeworkHomework
Text p. 462, #1-8 all, #10, #12, #16-30 Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36evens, #36
NJASK7 PrepNJASK7 Prep