2.
Essential Understanding andObjectives• Essential Understanding: to solve a system of equations, find a set of values that replace the variables in the equations and make each equation true.• Objectives:• Students will be able to solve linear system using a graph or table
3.
Iowa Core Curriculum• Algebra• A. CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.• A.CED.3 . Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.• A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.• A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
4.
System of Equations• System of equations: when you have two or more related unknowns, you can represent them with a set of two or more equations.• Linear System: consists of linear equations• Solution of a System: the set of values for the variables that makes all the equations true. • There could be one solution • Infinitely many solutions • No Solution• You can use a graph or table to solve a system of equations
5.
What is the solution? • Two different methods to solve: • Graphing • Table ì y = -x + 3ì x - 2y = 4 ïí í 3î3x + y = 5 ïy = x - 2 î 2 ì3x + y = 5 í îx - y = 7
6.
Example • If the growth rates• Greenland Shark continue, how long will Growth Rate: 0.75 cm/yr each shark be when it Birth Length: 37 cm is 25 years old?• Spiny Dogfish Shark • Explain why growth Growth Rate: 1.5 cm/yr rates for these sharks Birth Length: 22 cm may not continue indefinitely.• If the growth rates stayed the same at what age would the two sharks be the same length?
7.
Example • The table shows the populations of San Diego and Detroit. • Assuming the trends continue, when will the population of these cities be equal? What will the population be? • Step 1: Enter the Data into your lists on your calc • L1: Number of Years since 1950 • L2: San Diego population • L3: Detroit Population • Step 2: In the Stat Plot, turn on plots 1 and 2. In Plot 2 change list L2 to L3 by using the 2nd 3 (L3) to get the L3 list. Adjust window 1950 1960 1970 1980 1990 2000San Diego 334,387 573,224 696,769 875,538 1,110,549 1,223,400Detroit 1,849,568 1,670,144 1,511,482 1,203,339 1,027,974 951,270
8.
Example • The table shows the populations of San Diego and Detroit. • Assuming the trends continue, when will the population of these cities be equal? What will the population be? • Step 3: Calc the LinReg for both populations (you will need to type information into L2) • San Diego:17816x + 356896 • Detroit: -19217x + 1849401 • Step 4: Calculate intersection of the lines • Answer: 1990 and about 1,074,917 1950 1960 1970 1980 1990 2000San Diego 334,387 573,224 696,769 875,538 1,110,549 1,223,400Detroit 1,849,568 1,670,144 1,511,482 1,203,339 1,027,974 951,270
9.
Classifying a System of twoLinear Equations• Independent System: has one solution • Independent • 2 lines intersect at one point • the slopes of the lines are not equal • the y-intercepts may or may not be equal• Dependent System: has infinitely many solutions • Dependent • 2 lines coincide • the slopes of the lines are equal • the y-intercepts are equal• Inconsistent System: No Solution • Inconsistent • 2 parallel lines • the slopes of the lines are equal • the y-intercepts are not equal
10.
Example• Without graphing, is the system independent, dependent, or inconsistent?ì-3x + y = 4ïí 1ïx - y = 1î 3 ì2x + 3y = 1 í î 4x + y = -3 ì y = 2x - 3 í î6x - 3y = 9
Be the first to comment