1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Solving Systems Using Tables and Graphs
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
SOLVING SYSTEMS USING TABLES AND GRAPHS
Vocabulary System of equations – a set of two or more equations using the same variables.
Linear system – a set of two or more equations with the same variables.
Solution of a system – a set of values for the variables that makes all the equations true.
Inconsistent system – a system with no solution
Consistent system – a system with at least one solution.
Independent system – a system with a unique solution.
Dependent system – a system that does not have a unique solution.
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Categorizing Systems by Names Case
Number of Solutions
Name of System
Lines intersect
One
consistent independent
Parallel lines
Zero
inconsistent
Coinciding lines Infinitely many
consistent dependent
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Graphical Solutions of Linear Systems
Intersecting Lines y 6 5 4 3 2 1 6
5
4
3
2
1
One Solution Consistent Independent
x
0 1
1
2
3
4
5
6
2 3 4 5 6
Coinciding Lines y 6 5 4 3 2 1 6
5
4
3
2
1
x
0 1
1
2
3
4
5
6
Infinitely Many Solutions Consistent Dependent
2 3 4 5 6
Parallel Lines
y 6 5 4 3 2 1 6
5
4
3
2
1
0 1
x 1
2
3
4
5
No Solution Inconsistent
6
2 3 4 5 6
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Using a Graph or Table to Solve a System
EX #1: SOLVE BY GRAPHING METHOD: y 6 5 4 3 2 1 x 6
5
4
3
2
1
0 1
1
2
3
4
5
6
2 3 4 5 6
SOLVE BY TABLE METHOD:A system is “solved” where the yvalues are equal.
X
Y1
Y2
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Using a Table to Solve a Problem
EX #2: Alice bought 2 lbs of cheddar cheese and 3 lbs of turkey. She paid $26.35. Megan paid $18.35 for 1.5 lbs of cheese and 2 lbs of turkey. What was the price per pound of each item?
Define variables:
c = lbs. of cheddar cheese t = lbs. of turkey Write equations:
2c + 3t = 26.35 1.5 c + 2t = 18.35
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
One More Challenge EX #3: The enrollment for two high schools is shown below. If the trends continue when will the schools expect to have the same enrollment? What will the enrollment be?
Year 2005 2006 2007 2008 2009 2010
School A School B 628 432 632 436 627 461 621 477 615 488 612 498
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
USING TI84+ Operating System Version 2.55: PRESS:
STAT
1: Edit
1. Enter years from 2005 to 2010 as 0 to 5
2. Turn STAT PLOT on by pressing
2ND
Y =
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
3. View Data Plot in Quadrant 1 ZOOM
9:ZoomStat
4. Find Linear Regression Equations for School A and School B. STAT
CALC
4: LinReg(ax+b)
5. Move your cursor to Store RegEQ: Press
VARS
YVARS
1:Function 1: Y1
6. Move your cursor to Calculate and press ENTER, then GRAPH
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
7. Now, repeat steps 4 and 6 with Regression equation stored in Y2, using L1 for years and L3 School B enrollment
8. Press ENTER to Calculate and GRAPH
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
9. Reset window or use TABLE to find where the two lines intersect. This window has XMAX=15
10. Use Intersect feature Press:
2ND
TRACE
ENTER
ENTER
5:intersect
ENTER
11. Answer is 11 years after 2005 or in 2016, student enrollment will be about 589 students.
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Classifying a System Without Graphing EX #4: Without graphing, determine whether the system is independent, dependent, or inconsistent. Explain what this means graphically.
A.
y= 3x+4 y=3x - 3
B.
y = -2/3 x + 1/3
y= -4x -3
C.
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
Using Linear Regression
EX #5: The table shows the populations of San Diego and Detroit metropolitan regions. When were the populations of these regions equal? What was that population?
Populations of San Diego and Detroit Metropolitan Regions (1950 – 2000)
Year 1950 1960 1970 1980 1990 2000
San Diego 334,384 573,224 696,769 875,538 1,110,549 1,223,400
Detroit 1,849,568 1,670,144 1,511,482 1,203,339 1,027,974 951,270
Source: U.S. Census Bureau
STEP 1: Enter data into lists on your calculator. STEP 2: Use LinReg (ax + b) to find lines of best fit. STEP 3: Graph the linear regression lines. STEP 4: Use the Intersect feature.
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1 Solving Systems Using Tables and Graphs.notebook
October 19, 2012
DATA TABLE:
GRAPH:
40.3 years is about April 1990, population was around 1,074,858 people.
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