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Transcript
Notes 5.1 Graphing Systems of Equations I. Review: Solutions to Equations Think Pair Share • What is a solution to an equation in two variables? • What is the connection between an equation in two variables and it’s graph? • What is the connection between an equation and a point on its graph? • How many solutions does a linear equation have? • A solution to an equation in two variables is any pair of coordinates that makes the equation true. • If you plot all of the solutions to a linear equation on a coordinate plane, they form the line. All the points on the line are solutions to the equation- they make the equation true. • A linear equation as an infinite amount of solutions- there are an infinite amount of points on the graph. II. System of Equations A. What is it? A System of Equations: Two equations with the same variables, usually graphed on same coordinate plane. y 3x 2 y x 2 Where do they cross? (1, 1) What does that mean? (1, 1) is the only point that is a solution to BOTH equations. 2. Types/Number of Solutions III. Practice A. Naming Solutions 1. Use the graph to determine whether each system has no solution, one solution or infinitely many solutions. If it only has one solution, name it. One solution: (3, -1) 2. Use the graph to determine whether each system has no solution, one solution or infinitely many solutions. If it only has one solution, name it. Infinitely many solutions 3. Use the graph to determine whether each system has no solution, one solution or infinitely many solutions. If it only has one solution, name it. No solution B. Graphing and finding solutions 1. Graph the system of equations. Then determine whether each system has no solution, one solution or infinitely many solutions. If the system has one solution, name it. One Solution: (-1, -2) 2. Graph the system of equations . Then determine whether each system has no solution, one solution or infinitely many solutions. If the system has one solution, name it. One Solution: (2, 1) 3. Graph the system of equations . Then determine whether each system has no solution, one solution or infinitely many solutions. If the system has one solution, name it. Infinitely many solutions (same line) 3. Graph the system of equations. Then determine whether each system has no solution, one solution or infinitely many solutions. If the system has one solution, name it. No solution (parallel lines)