Solving Systems by Graphing

1
Solving Systems by Graphing
2
System of Linear Equations

• Two or more linear equations graphed on the same
  grid or pertaining to the same situation.

3
Solution of a System

• Any point common to all the lines is a solution.
• Any ordered pair that makes all the equations
  true is a solution of a system.

4
Solving Systems by Graphing

• Make sure both/all the equations are in the
  slope-intercept form (y mx b).
• Click on the moving calculator until you get a
  grid.
• Using either control g or clicking on the double
  arrows on the bottom left, enter the equations in
  f1 and f2
• You may have to menu gt 4 Window/Zoomgt 5 Zoom
  Standard to get it centered.
• If you cannot see the point of intersection, zoom
  out (Menu gt 4 Window/Zoom gt 4 Zoom Out).

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Solving Systems by Graphing

• Go to Menu gt 6 Analyze Graph gt 4 Intersection
• Lower Bound? Shows in the bottom left. Move the
  hand to the left of the point of intersection and
  click.
• Upper Bound? Shows in the bottom left. Move the
  hand to the right of the point of intersection
  and click.
• The ordered pair that shows near the point of
  intersection is the solution.
• Check by replacing the x and y with the
  appropriate numbers in both equations. The
  numbers should make BOTH equations true.

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Example 1

• Find the solution of this system by graphing
• y 2x 3
• y x 1
• Answer (2, 1)
• Check. Replace x with 2 and y with 1 in both
  equations
• 1 2(2) 3 True
• 1 2 1 True

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Example 2

• Solve y x 5
• y -4x
• Answer (-1, 4)
• Check Replace x with 1 and y with 4 in the
  first and second equations
• 4 -1 5 True
• 4 -1 x 4 True

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Try these

• y x 3
• y -x 1
• y -2x 1
• y x 5
• y 1/3x - 3
• y -2x 4

• (1, -2)
• (-2, 3)
• (3, -2)