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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

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Systems of linear equations

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  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

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