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Published byBritton Hawkins Modified over 6 years ago

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LESSON 5 – PROPERTIES OF LINEAR SYSTEMS SYSTEMS OF LINEAR EQUATIONS

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TODAYS OBJECTIVES Students will be able to solve problems that involve systems of linear equations in two variables graphically and algebraically, including: Explain, using examples, why a system of equations may have no solution, one solution, or an infinite number of solutions Explain a strategy to solve a system of linear equations Solve a problem that involves a system of linear equations

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VOCABULARY Infinite: endless amount or number, unlimited Coincident lines: two lines that have the same graph (same slope and y-intercept)

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PROPERTIES OF LINEAR SYSTEMS There are three possible solution sets in a system of linear equations: 1) One solution – Lines intersect once, different slopes 2) No solution – Parallel lines, same slope, different y-intercepts 3) Infinite solutions – same lines, same slopes, same y-intercepts

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PROPERTIES OF LINEAR SYSTEMS

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PROPERTIES OF LINEAR SYSTEMS

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PROPERTIES OF LINEAR SYSTEMS

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EXAMPLE One solution Infinite Solutions No Solutions

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CREATING A LINEAR SYSTEM WITH 0, 1, OR INFINITE SOLUTIONS

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CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

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CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

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YOUR TURN Create a linear system with no solutions, one solution, and infinite solutions, given the equation -6x + y = 3. Solutions:

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HOMEWORK pg. 448-449, #6, 8, 12-17, 19-20, 23 Next class we will have an assignment to be handed in for marks. The class after that, we will have a Chapter 7 test.

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ABCD QUIZ!

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