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: