Systems of Linear Equations

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Presentation transcript:

Systems of Linear Equations 7.6– PROPERTIES OF SYSTEMS OF LINEAR EQUATIONS

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

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

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

Properties of linear systems

Properties of Linear SYstems

Properties of Linear Systems

Example One solution Infinite Solutions No Solutions

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

Creating a linear system with 0,1, or infinite solutions

Creating a linear system with 0,1, or infinite solutions

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