System Linear Equation
University of Phoenix Material
Learning Team Summary Worksheet TWO (due week Five) Brenda Rivera
As a learning team, complete the table with formulas, rules, and examples from each section of Chapters 4, 5, 6,7,8,9,10 and 11 in the textbook. The completed summary will help prepare you for the Final Exam in Week 5. Points will be awarded for completion of the project.
Study Table for Weeks One and Two
Chapter 4 Systems of Linear Equations; Matrices (Section 4-1 to 4-6) | Examples | Reference (Where is it in the text?) | | | | DEFINITION: Systems of Two Linear Equations in Two VariablesGiven the linear system ax + by = hcx + dy = kwhere a , b , c , d , h , and k are real constants, a pair of numbers x = x0 and y = y0 [also written as an ordered pair (x0, y0)] is a solution of this system if each equation is satisfied by the pair. The set of all such ordered pairs is called the solution set for the system. To solve a system is to find its solution set. | EXAMPLE 1 Solving a System by Graphing Solve the ticket problem by graphing2x + y = 8x + 3 y = 9SOLUTION An easy way to find two distinct points on the first line is to find the x and y intercepts.Substitute y = 0 to find the x intercept (2x = 8, so x = 4), and substitute x =0 to find the y intercept (y = 8).Then draw the line through (4, 0) and (0, 8).After graphing both lines in the same coordinate system (Fig. 1), estimate the coordinates of the intersection point: | Page 170 | Systems of Linear Equations: Basic TermsDefinition: A system of linear equations is consistent if it has one or more solutions andInconsistent if no solutions exist. Furthermore, a consistent system is said to be independent if it has exactly one solution (often referred to as the unique solution ) and dependent if it has more than one solution. Two systems of equations are equivalent if they have the same solution set. | EXAMPLE 3 Solving a System Using a Graphing Calculator Solve to two
Learning Team Summary Worksheet TWO (due week Five) Brenda Rivera
As a learning team, complete the table with formulas, rules, and examples from each section of Chapters 4, 5, 6,7,8,9,10 and 11 in the textbook. The completed summary will help prepare you for the Final Exam in Week 5. Points will be awarded for completion of the project.
Study Table for Weeks One and Two
Chapter 4 Systems of Linear Equations; Matrices (Section 4-1 to 4-6) | Examples | Reference (Where is it in the text?) | | | | DEFINITION: Systems of Two Linear Equations in Two VariablesGiven the linear system ax + by = hcx + dy = kwhere a , b , c , d , h , and k are real constants, a pair of numbers x = x0 and y = y0 [also written as an ordered pair (x0, y0)] is a solution of this system if each equation is satisfied by the pair. The set of all such ordered pairs is called the solution set for the system. To solve a system is to find its solution set. | EXAMPLE 1 Solving a System by Graphing Solve the ticket problem by graphing2x + y = 8x + 3 y = 9SOLUTION An easy way to find two distinct points on the first line is to find the x and y intercepts.Substitute y = 0 to find the x intercept (2x = 8, so x = 4), and substitute x =0 to find the y intercept (y = 8).Then draw the line through (4, 0) and (0, 8).After graphing both lines in the same coordinate system (Fig. 1), estimate the coordinates of the intersection point: | Page 170 | Systems of Linear Equations: Basic TermsDefinition: A system of linear equations is consistent if it has one or more solutions andInconsistent if no solutions exist. Furthermore, a consistent system is said to be independent if it has exactly one solution (often referred to as the unique solution ) and dependent if it has more than one solution. Two systems of equations are equivalent if they have the same solution set. | EXAMPLE 3 Solving a System Using a Graphing Calculator Solve to two