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1.1 Solving Linear Systems by Graphing 9/14/12 Vocabulary System of 2 Linear Equations: A system consisting of two linear equations in two variables. Ex: 6x – 2y = 8 3x – y = 4 Solution of a system of 2 linear equations: Is an ordered pair (x, y) that satisfies both equations. Graphically, it’s the point where the lines intersect. Example 1 Solve a System by Graphing Solve the system by graphing. Then check your solution algebraically. Equation 1 3x – y = 3 ANSWER Equation 2 x + 2y = 8 ( 2, 3 ) Example 1 Solve a System by Graphing You can check the solution by substituting 2 for x and 3 for y into the original equations. Equation 1 Equation 2 3x – y = 3 x + 2y = 8 3( 2) – 3 =? 3 ? 8 2 + 2( 3) = ? 3 6 – 3= ? 8 2 +6 = 3=3 8=8 ANSWER The solution of the system is ( 2, 3 ). Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 1. y = – x + 3 y = 2x + 9 ANSWER ( –2, 5 ) Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 2. x – 3y = 1 –x + y = – 1 ANSWER ( 1, 0 ) Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 3. – x + 4y = 2 2x – 3y = 6 ANSWER ( 6, 2 ) Number of Solutions 1 solution : the lines have different slopes Infinitely many solutions :the lines have the same equation. No solution :the lines are parallel (same slope) Homework 1.1 #1, 3, 5, 7-14

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