Ordered Pairs


Jim worked twice as many hours as his sister Heather plus one more hour. Three times the number of hours Heather worked plus the amount of hours Jim worked equals six.



Example1
To solve this, we will set up two equations, graph them and find the point of intersection.


  • Let y equal hours worked by Jim.
  • Let x equal hours worked by heather.
  • Hours worked by Jim: y=2x+1
  • Hours worked by Heather: 3x+y=6
  • Graph y=2x+1
  • Graph 3x+y=6
  • The intersection of the two graphs is the solution.
  • The point (1,3) is the solution.
  • Jim worked 3 hours.
  • Heather worked 1 hour.
    		•  Graph of the equations



    Rule
  • If the two lines intersect, their is one solution.
  • If the two lines are parallel, there is no solution.
  • If the two lines coincide, there are an infinite number of solutions. Rule


    • Try graphing some on your own. Go to the Graph-It applet below. Find the solution to y = x+1 and 2x+y = 4.
    Ex. To graph y = x+1 and 2x+y = 4

  • Click on Set Graph
  • Set Range to -10, 10
  • Set Grid Lines to 1
  • Type in x+1
  • Put a Check in the box next to the function
  • In the next box type in -2 * x+4
  • Note: * must be used when multiplying
  • Put a Check in the box next to the function
  • The solution is their point of intersection.


    • Quick Hints:
    • X is the default domain variable.
    • Point to the graph to get exact values.


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