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* Linear/graphing question - Thanks!

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data

    L: 2x - y = 5
    M: x + y = 4

    So I got:

    L: y = 2x - 5
    M: y = -x + 4

    L has a slope of 2 and M has a slope of -1



    2. Relevant equations


    ****Now it says find the point of intersection on the graph. How do I plug those points on a graph? Any help would be GREAT!!!



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 23, 2010 #2

    berkeman

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    Staff: Mentor

    Good job. Now you have two equations and two unknowns (the x and y values that would be where the two lines meet). Have you studied how to solve systems of equations?

    Hint -- subtract the 2nd equation from the first one...
     
  4. Sep 23, 2010 #3
    Um, no we have not. Thats basically all it says in this certain practice question in our text book.

    Can u help me out on what to do next?

    Thanks, appreciate the help :)
     
  5. Sep 23, 2010 #4

    berkeman

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    Staff: Mentor

    Well, I gave you a hint already on how to solve those two equations simultaneously. You want to manipulate the equations so that you can eliminate one of the two variables, and that lets you get a number for the other one. So you listed your two equations:

    L: y = 2x - 5
    M: y = -x + 4

    Now just subtract the lower equation from the upper one. Like this:
    Code (Text):

      (y = 2x - 5)
    - (y = -x + 4)
    --------------
     
    Negate each term in the 2nd line (distribute the "-" sign through), and add the two lines. The +y and -y cancel to give you 0 on the left of the resulting equation, and you will end up with some x term and some constant term on the right. That lets you solve for x, and then you plug that value of x back into either of your first equations to find the value of y. You can check your x,y answer in both equations L and M to be sure that both equations are satisfied by that x,y point on the graphs. That is where the two lines cross, with a common x,y point.
     
  6. Sep 24, 2010 #5

    eumyang

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    Homework Helper

    How about graphing? Have you learned how to graph an equation of a line in slope-intercept form (y = mx + b)? If so, carefully graph the two lines on graph paper and see where they intersect.

    Or, if you have to solve the equations algebraically, the method shown above is solving by elimination. There's also a method known as solving by substitution. Start by setting one of the equations for one of the variables (already done in your case. Then substitute the equation you first manipulated into the other one for that variable. In your case, this means setting the two right sides equal:
    2x - 5 = -x + 4
    and solve for x. Then substitute the value for x in either of the original equation to solve for y.
     
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