1 / 13

Systems of linear equations

Systems of linear equations. Section 11.1. Types of systems. Unique Solution. No Solution. Infinite Number of Solutions. C onsistent System. Methods for solving systems. Graphing. Substitution. Elimination. Solve by Graphing. 1. - Independent Unique Solution

audrat
Download Presentation

Systems of linear equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Systems of linear equations Section 11.1

  2. Types of systems Unique Solution No Solution Infinite Number of Solutions Consistent System

  3. Methods for solving systems • Graphing • Substitution • Elimination

  4. Solve by Graphing 1. - Independent Unique Solution Consistent System

  5. Solve by Substitution 2. Solve an equation for a variable: Substitute that value into the other equation: Solve for the single variable. The solution is the point . Unique Solution Consistent System, Independent Equations Substitute that value into one of the original equations.

  6. Solve by Elimination 3. Multiply one or both equations by a nonzero number, so that the same variable in each equation has the same number coefficient with the opposite sign. Add the equations & solve for remaining variable: The solution is . Unique Solution Consistent System, Independent Equations Substitute that value into an original equation to solve for the remaining variable.

  7. Solve by Elimination 4.

  8. Inconsistent and Dependent Systems • If you have solved a system by Substitution or Elimination and obtain • A true statement like • the system is dependent and there are an infinite number of solutions. (SAME LINE) • A false statement like • the system is inconsistent and there is NO SOLUTION. (PARALLEL LINES)

  9. Inconsistent System The system is inconsistent. The lines do not intersect. 5. There is no solution. Solution:

  10. The system is dependent. Dependent system The graphs are the same line. There are an infinite number of solutions. Solution: Solve an equation for y: 6.

  11. College Student Spending 7. College student spend $183 more each year on textbooks and course materials than on computer equipment. They spend a total of $819 on textbooks and course materials and on computer equipment each year. (Source: National association of College Stores) How much is spent each year on textbooks and course materials and how much is spent on computer equipment? x = amount of money spent on textbooks and course materials y = amount of money spent on computer equipment Solve by elimination.

  12. Museum admission prices 8. Indianapolis Children’s Museum costs $5 more for an adult than for a child. Admission to the museum for Barbara and Jeff Johnson and their five children costs $59. Find the cost of each adult’s admission and each child’s admission. x = cost of adult admission y = cost of child admission

  13. Mail-order business 9. A mail-order lacrosse equipment business shipped 120 packages one day. Customers are charged $3.50 for each standard-delivery package and $7.50 for each express-delivery package. Total shipping charges for the day were $596. How many of each kind of package were shipped? x = # of standard-delivery packages y = # of express-delivery packages

More Related