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1.1 Solving Linear Systems by Graphing 9/14/12

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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. Vocabulary System of 2 Linear Equations: A system consisting of two linear equations in two variables. Ex: 6x – 2y = 8 3x – y = 4

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Example 1 Solve a System by Graphing Solve the system by graphing. Then check your solution algebraically. 33x3x–y = 8x+2y2y = Equation 1 Equation 2 ANSWER () 2, 3

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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 1Equation 2 33x3x–y = 8x+ 2y2y = () 233–3 = ? 28 + = ? () 32 36–3 = ? 28 + = ? 6 33 = 88 = ANSWER ( ).). 2, 3 The solution of the system is

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Checkpoint Solve the system by graphing. Then check your solution. 1. 3y–x = + 9 y 2x = + ANSWER () 2, 5 – Solve a System by Graphing

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Checkpoint 2. x3y3y = – 1 xy = + 1 –– ANSWER () 1, 0 Solve a System by Graphing Solve the system by graphing. Then check your solution.

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Checkpoint 3. = 2x2x3y3y = – 6 ANSWER () 6, 2 Solve a System by Graphing Solve the system by graphing. Then check your solution. 2+4y4yx –

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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)

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Homework 1.1 #1, 3, 5, 7-14

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