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UNIT 6.15 Special Solutions: Graphing I can identify special solutions within a system of equations graphically.

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Vocabulary (review) One Solution of a System of Linear Equations: The intersection of all lines in the system. Or the values of the variables that are true for all equations in the system. Example: (1, 2) The solution of this linear system is (1, 2) or when x = 1, y = 2.

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Vocabulary No Solution: A System of Linear Equations can have no solution when there is no point of intersection of the lines (i.e. when the lines are… ). Example: There is no solution in this linear system because there is no point of intersection! Parallel

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Vocabulary Infinite Solutions: A System of Linear Equations can have infinite solutions when the equations describe the same line (i.e. when the lines … ) Example: There are infinite solutions in this linear system because the intersection includes ALL points on the line! Coincide

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We already know we can solve Systems of Linear Equations graphically. Let’s try it with a method I call the Graph-and-check method. First, you …

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GRAPH IT … (3, -1)

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Then you CHECK IT! (3, -1) When we substitute the values of the variables back into each equation, does it hold true? Does -1 = -(3) + 2 ? Does -1 = 3 – 4 ? Yes

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GRAPH IT … Infinite Solutions!

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Now, CHECK IT! When we substitute in a point (x, y) that works for one equation, does it work for the other one? Yes Let’s try (1, -2). Does (-2) + 1 = -(1) ? Does (1) + (-2) = -1 ?

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GRAPH IT … No solution!

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Now, CHECK IT! Are the lines PARALLEL? No solution!

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Graph & Check #1 (3, 5) ClearBoards!

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Graph & Check #2 No Solution! ClearBoards!

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Graph & Check #3 No solution! ClearBoards!

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Graph & Check #4 (1, 3) ClearBoards!

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Graph & Check #5 Infinite solutions! ClearBoards!

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6.15 GRAPHING SPECIAL SOLUTIONS WS Homework Time! I can identify special solutions within a system of equations graphically.

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