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    e.g. for 2x - 3y = 6

    I think I can do this to find the root (putting 0 in for y)

    2x - 3y = 6
    2x - 3(0) = 6
    2x = 6
    x = 3

    But when you have one more term e.g. 4x+3y+12=0 could you still use the same "method"?

    4x + 3y(0) + 12 = 0
    4x + 12 = 0
    12/-4x = -3 (or something? )
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    (Original post by tymbnuip)
    e.g. for 2x - 3y = 6

    I think I can do this to find the root (putting 0 in for y)

    2x - 3y = 6
    2x - 3(0) = 6
    2x = 6
    x = 3

    But when you have one more term e.g. 4x+3y+12=0 could you still use the same "method"?

    4x + 3y(0) + 12 = 0
    4x + 12 = 0
    12/-4x = -3 (or something? )

    they're the same type of question

    2x - 3x = 6 can be written as 2x - 3x - 6 = 0,

    just as 2x + 3y + 12 = 0 can be written as 2x + 3y = -12.
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    yes you can!

    4x + 3y(0) + 12 = 0
    4x + 12 = 0
    x = -3

    however, do remember that these equations have infinitely many solutions.

    for eg, x = 0, y = -4 is also a solution to the second problem. if you plot these points on a graph, you will get a straight line.
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    So can I then find a "slope"?
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    rewrite the equation in the form:
    y = mx+c,
    then, slope = m
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    4x + 3y + 12 =0
    3y= -4x - 12
    y= -4/3x - 4

    Then you get the 'slope', which is -4/3
    (Haven't done any maths during summer so hope my answer is right lol )
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    (Original post by thomaskurian89)
    yes you can!

    4x + 3y(0) + 12 = 0
    4x + 12 = 0
    x = -3

    however, do remember that these equations have infinitely many solutions.

    for eg, x = 0, y = -4 is also a solution to the second problem. if you plot these points on a graph, you will get a straight line.
    I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
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    (Original post by RichE)
    I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
    Yep I agree :yep:
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    So is the root still (-3,0) for 4x+3y+12=0?
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    (Original post by tymbnuip)
    So is the root still (-3,0) for 4x+3y+12=0?
    Yep. You'd probably just call the root "3" or "x = 3" though, as a root is always when y = 0.
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    (Original post by RichE)
    I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
    Root of an equation - (Alg.) that value which, substituted for the unknown quantity in an equation, satisfies the equation. (http://www.thefreedictionary.com/Root+of+an+equation)

    thereafter, the equation 4x + 12 = 0 has only one solution whereas
    the equation 4x + 3y + 12 = 0 has infinitely many solutions.
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    So for 2x-3y=6 (to find the slope) I would rewrite as 2x-3y-6=0.

    Then rewrite in form y = mx+c.

    2x - 3y - 6 = 0
    3y= -2x - 6
    y= -2/3x - 2 = -2/3 for slope? Though the answer doesn't have a minus in apparently - why has mine got a negative in? (n00b question)
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    (Original post by thomaskurian89)
    thereafter, the equation 4x + 12 = 0 has only one solution whereas
    the equation 4x + 3y + 12 = 0 has infinitely many solutions.
    I think the implication is that a "root" is when y = 0, so although 4x + 3y + 12 = 0 has infinitely many solutions (x, y), it has only one root (-3).
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    (Original post by tymbnuip)
    3y= -2x - 6
    incorrect.

    3y= 2x - 6
    m=2/3
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    (Original post by tymbnuip)
    So for 2x-3y=6 (to find the slope) I would rewrite as 2x-3y-6=0.

    Then rewrite in form y = mx+c.

    2x - 3y - 6 = 0
    3y= -2x - 6
    y= -2/3x - 2 = -2/3 for slope? Though the answer doesn't have a minus in apparently - why has mine got a negative in? (n00b question)
    You've made a sign error in moving to the bit I've put in bold. The method is correct, however.

    Also, the equals sign I've put in red isn't correctly used. y doesn't equal -2/3 (which your equals sign implies), the slope does. You could've written "therefore" where the equals sign is. It's a bad habit to get into, as it looks bad, it's incorrect and you'll get marked down in exams for it.
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    (Original post by tommm)
    I think the implication is that a "root" is when y = 0, so although 4x + 3y + 12 = 0 has infinitely many solutions (x, y), it has only one root (-3).
    We usually talk about roots in equations of one variable. For example, x = 0 and x = 5 are roots of the equation x2 -5x = 0

    when there are multiple variables, and too few equations there are infinitely many solutions.
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    (Original post by Green Clover)
    4x + 3y + 12 =0
    3y= -4x - 12
    Are the signs right in this ? i.e. should it be

    3y = 4x +12
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    Anyone? :o:
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    What Green Clover put is correct.
 
 
 
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