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Math Help - Help Me

  1. #1
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    Post Help Me

    ok i know how to this but i donno if i did right

    3y-x=3 and 4x+3y-18=0


    -solve by graphing
    -solve using algebra
    -and formal check
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  2. #2
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    Quote Originally Posted by usm_67
    ok i know how to this but i donno if i did right

    3y-x=3 and 4x+3y-18=0


    -solve by graphing
    -solve using algebra
    -and formal check
    Hello,

    to graphing: I've attached a drawing. The coordinates of the intersection is the solution you're looking for.

    to using algebra: There are at least 4 to 5 different method to get a solution:
    3y-x=3\ \Longleftrightarrow \ y= \frac{1}{3} x+1
    4x+3y-18=0\ \Longleftrightarrow \ y= - \frac{4}{3} x+6

    Both values of y must be equal:

     \frac{1}{3} x+1 = - \frac{4}{3} x+6
     \frac{5}{3} x =5 and that means: x = 3

    Put x = 3 in one the equations: y= \frac{1}{3} 3+1=2

    So you get the intersection at (3,2)

    to formal check: Put x=3 and y=2 in your original equations:

    3y-x=3\ \Longrightarrow \ 3 \cdot 2-3=3 you'll get 3=3 and that's true.

    4x+3y-18=0\ \Longrightarrow \ 4 \cdot 2 + 3 \cdot 3 -18=0 You'll get: 12 + 6 -18=0 and that's true.

    Greetings

    EB
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  3. #3
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    thanks a lot but dosent it have to do with

    Elmination and Substitution as well
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  4. #4
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    Quote Originally Posted by usm_67
    thanks a lot but dosent it have to do with

    Elmination and Substitution as well
    Hello,

    here I'm again. Of course you're right. But as I mentioned before there are many different methods. So if you have to use elimination and substitution, you can do it like this:

    3y-x=3\ \Longleftrightarrow \ y= \frac{1}{3} x+1

    Put this value of y into the 2nd equation to eliminate the variable y:

    4x+3\cdot \left( \frac{1}{3} x+1 \right)-18=0\ \Longrightarrow \  4x+x+3-18=0

    Simplify this equation and you'll get: 5x - 15 = 0. That means: 5x = 15 and so x = 3

    Put this value into the 1rst equation and you'll get y = 2

    And that's the result you've got before.

    It doesn't matter which method you use, all of them come to the same solution.

    Greetings

    EB
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