01a3 Solving Graphically.notebook February 08, 2016 Unit 1 ­ Systems of Linear Equations Feb 6­11:29 PM Consider: A linear relation can be represented graphically as a straight line. A straight line is made up of an infinite number of points, (x, y), connected together. Some other straight line would be made up of an infinite number of different points. What does it mean for these lines to intersect? Sep 13­10:53 PM 1 01a3 Solving Graphically.notebook February 08, 2016 Unit 1 ­ Systems of Linear Equations Solving Linear Systems Graphically The graph of a linear relation forms a straight line. Two (or more) linear relations can be graphed together, forming a linear system. The solution to a linear system is the point (x,y) where the lines intersect (or cross) each other. line b Point of Intersection (solution) line a solve graphically a) Feb 9­8:53 PM 2 01a3 Solving Graphically.notebook February 08, 2016 a) Feb 9­8:53 PM b) Feb 9­8:54 PM= 3 01a3 Solving Graphically.notebook February 08, 2016 b) Not all solutions will have 'nice' values. These can be difficult, or impossible, to solve graphically. Feb 9­8:54 PM= c) #3, #4 4 01a3 Solving Graphically.notebook February 08, 2016 c) #3, #4 d) #1, #2 5 01a3 Solving Graphically.notebook February 08, 2016 d) #1, #2 In Summary: For no solution: ­ same slope and different y­intercepts For exactly one solution: ­ different slopes only ­ some graphical systems can only be solved exactly using technology For infinitely many solutions: ­ same slope and same y­intercept summary 6 01a3 Solving Graphically.notebook February 08, 2016 Assigned Work: p. 26 # 2(i)(abc), 3ab, 5abf, 10, 18* hw 7 Attachments Basic 2D Grid.agg