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Notes for Lesson 6-1: Solving Systems by Graphing 6-1.1 – Identifying Solutions of Systems Vocabulary: System of linear equations – a system of equations in which all of the equations are linear Solution of a system of linear equation – any ordered pair that satisfies all the equations in a system A system of linear equations are 2 or more linear equation that are related to each other in some way. A lot of times we want to be able to solve these systems simultaneously or at the same time. When that happens we need to find a value for x and y that will make both equation true at the same time. Examples: Tell whether the ordered pair is a solution of the given system 2x 5 y 8 3x 2 y 5 x 2y 6 x y 3 Plug the x and y values into both equation and see if they work. 1,2 ; (4) 2(1) 6 2(1) 5(2) 8 4,1 ; 4 1 3 3(1) 2(2) 5 2 10 8 3 4 5 88 7 5 Both are not true so it is not a solution 42 6 33 66 Both are true so it is a solution 6-1.2 – Solving a system of linear equations by graphing All of the ordered pairs that make a linear equation true are on its graph. So we need to find a point that is on both of the line graphs, in other words we need the point of intersection of the two lines. Examples: Solve each system by graphing 5 4 y x 3 y x 1 The lines cross at 1,2 so that is the solution y 2 -5 -4 -2 2 4 5 2 4 5 x -2 -4 -5 x y 0 1 y x 1 2 5 4 The lines cross at 2,2 so that is the solution 2 -5 -4 -2 -2 -4 -5 y x 6-1.3 – Problem solving application Bowl-o-Rama charges $2.50 per game plus $2 for shoe rental, and Bowling Plaza charges $2 per game plus $4 for shoe rental. For how many games will the cost to bowl be the same at both places? Write the equations: Bowl-a-Rama: y 2.50 x 2 Bowling Plaza: y 2 x 4 20 Graph both linear equations: 18 16 14 12 10 8 6 4 2 0 y x 0 2 4 6 8 10 12 14 16 18 20 The numbers of games would be 4 for a cost of $12 Practice B #’s 1, 3, 4, 5