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Math Help - How Can I Solve Linear Equations Graphically, Not Algebretically??

  1. #1
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    How Can I Solve Linear Equations Graphically, Not Algebretically??

    Ive been given a graph to plot my 2 lines, and find the point of intersection. I have 2 equations naturally, and they go like this.

    2x + 5y= 10
    3x + 2y=-2

    How do I go about this? Im also assuming once I solve these algebretically the point of intersection on the graph will be the points I get from the algebretic part. Much thx peeps I really need this.
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  2. #2
    dan
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    solve foe y in each quation and graph them bolth.....

    if you solve algebreticlly first you will have a more precice anwer...

    dan
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  3. #3
    dan
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    graph the equations y=(10 -2x)/5 and y=(-2 - 3x)/3

    the graphs cross at (-4.444 , 3.777)

    this is your answer

    have a nice day^_^

    dan
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    ya but if I solve them algebretically I only get 1x value and 1 y value,
    x=30/-11 and y=34/11, which are both numbers with like 10 decimals.

    Im suppose to graph each equation as a line then get the point of intersection.
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  5. #5
    dan
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    Quote Originally Posted by NemesysEvolved View Post
    ya but if I solve them algebretically I only get 1x value and 1 y value,
    x=30/-11 and y=34/11, which are both numbers with like 10 decimals.

    Im suppose to graph each equation as a line then get the point of intersection.
    go ahed and graph them...plot some values for each equation. the quations are liner and should only cross once...


    dan
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  6. #6
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    Quote Originally Posted by dan View Post
    graph the equations y=(10 -2x)/5 and y=(-2 - 3x)/3

    the graphs cross at (-4.444 , 3.777)

    this is your answer

    have a nice day^_^

    dan
    ok but how can I possibly put those on a point on a piece of graph paper, their not even whole numbers there an undefined value in it being x. I need to have a point for x and a point for y on each equation so I can make 2 straight lines from each equation and get the point of intersection.
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  7. #7
    Senior Member OReilly's Avatar
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    Quote Originally Posted by NemesysEvolved View Post
    Ive been given a graph to plot my 2 lines, and find the point of intersection. I have 2 equations naturally, and they go like this.

    2x + 5y= 10
    3x + 2y=-2

    How do I go about this? Im also assuming once I solve these algebretically the point of intersection on the graph will be the points I get from the algebretic part. Much thx peeps I really need this.

    Solve both equations for y:
    1) y=(10-2x)/5
    2) y=(-2-3x)/2

    I have made a graph.

    Blue line represents equation 2x + 5y= 10 and red line 3x + 2y=-2.

    Dan has right answer (-4.444 , 3.777), but my graph doesn't show that x = -4.444.
    I am puzzled by that, graph was from MS Excel. In graph clearly can be seen that x is between -2 and -4. That is error, maybe bug in MS Excel.
    Attached Thumbnails Attached Thumbnails How Can I Solve Linear Equations Graphically, Not Algebretically??-image1.jpg  
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  8. #8
    dan
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    Quote Originally Posted by OReilly View Post
    Solve both equations for y:
    1) y=(10-2x)/5
    2) y=(-2-3x)/2

    I have made a graph.

    Blue line represents equation 2x + 5y= 10 and red line 3x + 2y=-2.

    Dan has right answer (-4.444 , 3.777), but my graph doesn't show that x = -4.444.
    I am puzzled by that, graph was from MS Excel. In graph clearly can be seen that x is between -2 and -4. That is error, maybe bug in MS Excel.
    my calc got a defferent graph... i'm doing the graphs on my laptop and writing you on a frends computer so i cant show you but there must be a bug...

    dan
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  9. #9
    dan
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    Quote Originally Posted by NemesysEvolved View Post
    ok but how can I possibly put those on a point on a piece of graph paper, their not even whole numbers there an undefined value in it being x. I need to have a point for x and a point for y on each equation so I can make 2 straight lines from each equation and get the point of intersection.
    you don't need to plot a whole number... just plot where the graphs intersect and lable the point (-4.44444,3.7777777)

    then sighn it and give it to your teacher tada...

    if you are still having truble let us know...

    dan
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  10. #10
    Senior Member OReilly's Avatar
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    Quote Originally Posted by dan View Post
    my calc got a defferent graph... i'm doing the graphs on my laptop and writing you on a frends computer so i cant show you but there must be a bug...

    dan
    Actually your algebraic answer is wrong, I calculated now.

    2x + 5y= 10 ---> x=(10-5y)/2
    3x + 2y=-2 ---> x=(-2-2y)/3

    (2-2y)/3=(10-5y)/2
    2(-2-2y)=3(10-5y)
    -4-4y=30-15y
    11y=34
    y=34/11
    y=3.09

    3x+2*3.09=-2
    3x+6.18=-2
    3x=-2-6.18
    x=-8.18/3
    x=-2.72

    So correct answer is (-2.72, 3.09).

    MS Excel graph that I putted is correct.
    Last edited by OReilly; September 26th 2006 at 05:12 PM. Reason: Forgot to put minus sign in x.
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  11. #11
    Forum Admin topsquark's Avatar
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    You guys need to check your algebra. I'm getting:
    (x,y) = (-30/11, 34/11) = (-2.73, 3.09)
    which matches the graph.

    -Dan

    (Ya beat me! )
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  12. #12
    Senior Member OReilly's Avatar
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    Quote Originally Posted by topsquark View Post
    You guys need to check your algebra. I'm getting:
    (x,y) = (-30/11, 34/11) = (-2.73, 3.09)
    which matches the graph.

    -Dan

    (Ya beat me! )
    I have doubted first in MS Excel graph, trusting dan more than Bill Gates, but Bill won this time!

    And I forgot to round x . x = - 2.73 not -2.72
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  13. #13
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    Quote Originally Posted by OReilly View Post
    I have doubted first in MS Excel graph, trusting dan more than Bill Gates, but Bill won this time!

    And I forgot to round x . x = - 2.73 not -2.72
    ok so how do I plot numbers into each equation when each equation is put into x=10-5y/2, and x=(-2-2y)/3, becaue I just made my own values for y then used to coordinates for xand y that i got from each equation and put them on my graph, but the point of intersection is nowhere near the x=-2.73 and the other u mentioned.So what am I doing wrong here?

    What I did here was put y=4 into the 1st equation, and got the coordinates (-5,4) and for the second I put y=6 into it, and got (-4.6666667,6), when I put those on the graph my points of intersection were (-3.8, 0.9) roughly
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  14. #14
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    Quote Originally Posted by NemesysEvolved View Post
    ok so how do I plot numbers into each equation when each equation is put into x=10-5y/2, and x=(-2-2y)/3, becaue I just made my own values for y then used to coordinates for xand y that i got from each equation and put them on my graph, but the point of intersection is nowhere near the x=-2.73 and the other u mentioned.So what am I doing wrong here?

    What I did here was put y=4 into the 1st equation, and got the coordinates (-5,4) and for the second I put y=6 into it, and got (-4.6666667,6), when I put those on the graph my points of intersection were (-3.8, 0.9) roughly
    I am not sure what you did but you should take for both equations values lets say from -5 to 5 for y and calculate x and you get coordinates you can put on graph.

    So, take first equation x=10-5y/2 and calculate all values x for y={-5,-4,-3,...5} and draw line on graph and do again for second equation and you will get intersection.
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  15. #15
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    can you tell me if im solving this right, there is 2 different ways I can enter this in my calculator and I get 2 different answers.


    x=10-5y/2
    im gonna sub y for 1
    x=10-5(1)/2 so that equals 2.5, so the coordinates are (2.5,1)
    now if you calculate the value of y using the same equation but subbling in y=2, I get the coordinates (0,2), then if I sub in y=3 i get the coordinates (-2.5,3) That line does not line up on the graph!! Im lost completely it seems so simple but isnt.
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