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WARM-UP Complete the below problems. A) Find a solution to the linear equation: y 2 x 1 y 3 x 2 B) Sketch a graph of: 3.1: SOLVING SYSTEMS USING TABLES AND GRAPHS TODAY’S OBJECTIVE LINEAR SYSTEMS • To solve a linear system using a graph or table Systems of equations: A set of 2 or more equations 4 X Y1 Y2 2 -5 5 Linear system: Consists of linear equations Solution: A set of values for all variables that makes all the equations in the system true. Also known as the intersection point of the lines. -2 -4 METHOD: SOLVE BY GRAPHING METHOD: SOLVE BY CREATING A TABLE x 4 2 x 2y 4 3x y 5 2 y x 4 y 3 x 5 1 y x2 2 . 5 1 y1 x 2 2 y 2 3 x 5 Y1 Y2 -2 -3 -1 -2.5 0 -2 11 8 5 1 -1.5 2 2 -1 -1 -2 -4 The lines have one intersection point. Therefore, the solution is (2,-1) We look for where the y-values are equal and use those values to create the ordered pair for our solution: (2,-1). This system is classified as independent. 1 CLASSYIFYING SYSTEMS: INCONSISTENT 3 x y 4 y 2x 3 4 1 x y 1 3 x 1 y 1 3 -5 -5 5 3 x y 3 -2 y 3x 3 -4 When a system contains parallel lines, there is no solution. WRAP-UP Consistent Dependent – Infinitely Many Solutions Systems No Solution – Parallel Lines Inconsistent 6x 3y 9 3 y 6 x 9 y 2x 3 -5 -5 55 -2 -2 -4 -4 When a system contains coinciding lines, there are infinitely many solutions. Coach Lee offers tennis lessons at $25 per hour. The Hunterdon Tennis Club charges $20 per hour and a registration fee of $10. A) Write a system of equations that represents the cost of tennis lessons in terms of hours. B) When are the costs the same? C) If you plan on practicing 10 hours a week, which option is better? TONIGHT’S HOMEWORK APPLYING THE LESSON c 25h PAGES 138-139 c 20h 10 7 – 9 & 12 (Create a table), 17-27 odd, 29 – 32 x B) 2 hours of instruction 22 APPLYING THE LESSON Independent – One Solution A) 44 6x 3y 9 2 3 x y 4 y 3x 4 CLASSYIFYING SYSTEMS: DEPENDENT Y1 Y2 0 0 10 1 25 30 2 50 50 3 75 70 C) Hunterdon Tennis Club 2