Results 1 to 7 of 7

Math Help - linear equations

  1. #1
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1

    linear equations

    this is the question

    John bought 3 shirts and 4 pairs of socks for $78.
    Joan bought 2 shirts and 6 pairs of socks for $72.

    Letting $x equal the price of a shirt and $y equal the price of a pair of socks, write a linear equation to represent each transaction.
    Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

    i came up with this
    3x + 4y = 78

    2x+ 6y = 72

    howeve, im not sure how do the graphany help on this ould be cool

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37
    3x + 4y = 78
    2x+ 6y = 72

    Lets arrange these two equations such that they are in y=mx+b form.

    3x + 4y = 78
    4y = 78 - 3x
    4y = 3(26-x)
    y = (3/4) (26-x)

    2x+6y = 72
    6y = 72-2x
    6y = 2 (36-x)
    y = (1/3) (36-x)

    Now can you graph these? If you must, you can always google "online graphing calculator" or something like that.

    To find the point of intersection, let's just set the two equations (in y=mx+b form) equal to one another. So, we have: (3/4) (26-x) = (1/3) (36-x). Find x and then plug in your value for x into either of the equations to determine your y-value. Then you will have your point of intersection in the form (x,y).

    -Andy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by realistic View Post
    this is the question

    John bought 3 shirts and 4 pairs of socks for $78.
    Joan bought 2 shirts and 6 pairs of socks for $72.

    Letting $x equal the price of a shirt and $y equal the price of a pair of socks, write a linear equation to represent each transaction.
    Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

    i came up with this
    3x + 4y = 78

    2x+ 6y = 72

    howeve, im not sure how do the graphany help on this ould be cool

    Quote Originally Posted by abender View Post
    3x + 4y = 78
    2x+ 6y = 72

    Lets arrange these two equations such that they are in y=mx+b form.

    3x + 4y = 78
    4y = 78 - 3x
    4y = 3(26-x)
    y = (3/4) (26-x)

    2x+6y = 72
    6y = 72-2x
    6y = 2 (36-x)
    y = (1/3) (36-x)

    Now can you graph these? If you must, you can always google "online graphing calculator" or something like that.

    To find the point of intersection, let's just set the two equations (in y=mx+b form) equal to one another. So, we have: (3/4) (26-x) = (1/3) (36-x). Find x and then plug in your value for x into either of the equations to determine your y-value. Then you will have your point of intersection in the form (x,y).

    -Andy
    Great work abender! Here's a graph to verify what you have done:



    --Chris
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1
    Quote Originally Posted by Chris L T521 View Post
    Great work abender! Here's a graph to verify what you have done:



    --Chris
    i can see now for:

    3x + 4y =78
    y = -(3/4)x + 19.5

    2x + 6y = 72
    y = -(1/3)x +12

    could you please explain :

    {x, -0, 20} this part
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by realistic View Post
    i can see now for:

    3x + 4y =78
    y = -(3/4)x + 19.5

    2x + 6y = 72
    y -(1/3)x +12

    could you please explain :

    {x, -0, 20} this part
    Oh. That last bit is code that is required for mathematica to plot the graph. I input some domain, and it graphs the set of functions within that specified domain. It has nothing to do with the problem.

    The stuff above the graph is the code that outputs the graph.

    I hope that this didn't cause much confusion...

    --Chris
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1
    Quote Originally Posted by Chris L T521 View Post
    Oh. That last bit is code that is required for mathematica to plot the graph. I input some domain, and it graphs the set of functions within that specified domain. It has nothing to do with the problem.

    The stuff above the graph is the code that outputs the graph.

    I hope that this didn't cause much confusion...

    --Chris
    In the question it also asks me to write a linear equation to represent each transaction. (which I understand thanks to you guys)

    But also I have to:

    Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

    this part im struggling with
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by realistic View Post
    In the question it also asks me to write a linear equation to represent each transaction. (which I understand thanks to you guys)

    But also I have to:

    Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

    this part im struggling with
    What you would need to do is this:

    You know what the y intercepts are from the equations.

    What we need to find now is where they cross the x axis. Then drawing the line is a piece of cake.

    To do this, set y in both equations equal to 0:



    This tells us where they will cross the x axis. The graph verifies this:



    Again, don't get confused, the top part of the graph is the code that generates the graph...

    To find the intersection point, set the two equations equal to each other:



    The graph verifies what we have done:



    Does this make more sense now?

    --Chris
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: November 30th 2011, 02:41 AM
  2. Linear Alegebra linear equations proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 13th 2010, 10:47 AM
  3. Replies: 7
    Last Post: August 30th 2009, 11:03 AM
  4. Replies: 3
    Last Post: February 27th 2009, 08:05 PM
  5. Replies: 1
    Last Post: July 29th 2007, 03:37 PM

Search Tags


/mathhelpforum @mathhelpforum