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Graphs and Applications of Linear Equations
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Ordered Pairs
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To graph ordered pairs of real numbers, we need a coordinate system.
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The rectangular or Cartesian coordinate system
Ordered Pairs The rectangular or Cartesian coordinate system
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Ordered Pairs The rectangular or Cartesian coordinate system consists of a horizontal number line, the x-axis
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Ordered Pairs The rectangular or Cartesian coordinate system consists of a horizontal number line, the x-axis and a vertical number line, the y-axis
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x - axis
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x x - axis
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x x - axis
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y - axis x x - axis
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y y - axis x x - axis
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y x
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y x
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y x
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y Origin x
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y Origin x
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y Origin x
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y P (a,b) Origin x
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y P (a,b) Quadrant I Origin x
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y P (a,b) Quadrant II Quadrant I Origin x
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y P (a,b) Quadrant II Quadrant I Origin x Quadrant III
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y P (a,b) Quadrant II Quadrant I Origin x Quadrant III Quadrant IV
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Quadrant I
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Quadrant I
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Quadrant I
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y Quadrant II Quadrant I x Quadrant III Quadrant IV
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Quadrant II
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Quadrant II
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Quadrant II
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y Quadrant II Quadrant I x Quadrant III Quadrant IV
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Quadrant III
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Quadrant III
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Quadrant III
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y Quadrant II Quadrant I x Quadrant III Quadrant IV
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Quadrant IV
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Quadrant IV
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y Quadrant II Quadrant I x Quadrant III Quadrant IV
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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x Quadrant I Locate on the
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in Quadrant I x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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x Quadrant III Locate on the
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x Quadrant III
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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x Quadrant II Locate on the
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in Quadrant II x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair x
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y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
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x Quadrant IV Locate on the
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x Quadrant IV
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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y Find the coordinates of the point x
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Determine whether each of the following pairs is a solution of
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (3,7) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (0,1) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Show that the pair (-3,-5) is a solution of the equation
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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Then graph the three points and use the graph to determine another pair that is a solution.
y x
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