3.1 Solving Linear Systems by Graphing

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3.1 Solving Linear Systems by Graphing
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Objectives/Assignment

• Graph and Solve systems of linear equations.
• Assignment 11-31 odd, 32-34 all, 35-51 odd

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Warm Up
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System of 2 linear equations (in 2 variables x
y)

• 2 equations with 2 variables (x y) each.
• Ax By C
• Dx Ey F
• Solution of a System
• an ordered pair (x,y) that makes both equations
  true.

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Ex Check whether the ordered pairs are solution
of the system.x-3y -5-2x3y10

• (-5,0)
• -5-3(0) -5
• -5 -5
• -2(-5)3(0)10
• 1010
• Solution

• (1,4)
• 1-3(4) -5
• 1-12 -5
• -11 -5
• doesnt work in the 1st eqn, no need to check
  the 2nd.
• Not a solution.

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Solving a System Graphically

• Graph each equation on the same coordinate plane.
  
• If the lines intersect The point (ordered pair)
  where the lines intersect is the solution.
• If the lines do not intersect
• They are the same line infinitely many
  solutions (they have every point in common).
• They are parallel lines no solution (they share
  no common points).

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Ex Solve the system graphically.2x-2y
-82x2y4
(-1,3)
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Ex Solve the system graphically.2x4y12x2y6

• 1st eqn
• 2ND eqn
• What do you notice about the equations?
• the 2 equations are for the same line!
• many solutions

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Ex Solve graphically x-y5 2x-2y9

• 1st eqn
• 2nd eqn
• What do you notice about the lines?
• They are parallel! Go ahead, check the slopes!
• No solution!