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**Systems of Linear Equations**

7.6– PROPERTIES OF 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: Coincident lines:**

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

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