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Math Help - Solving equations - to Graph!

  1. #1
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    Solving equations - to Graph!

    How do you solve these corresponding equations (will use the values of y and x to graph)

    3x-y-=5 and x+3y=6

    I've figured out how to solve 3x-y=5 by doing this:
    3x-y=5
    y=3x-5

    But what about the other one? (x+3y=6)
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  2. #2
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    Quote Originally Posted by cnmath16 View Post
    How do you solve these corresponding equations (will use the values of y and x to graph)

    3x-y-=5 and x+3y=6

    I've figured out how to solve 3x-y=5 by doing this:
    3x-y=5
    y=3x-5

    But what about the other one? (x+3y=6)
    Solve the second equation for y:

    x+3y=6~\implies~3y=-x+6~\implies~y=-\dfrac13 x + 2

    Now draw the graphs of these equations. The coordinates of the intersection point are the solutions of both equations.

    According to my sketch I got x = 2.1 and y = 1.3
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by cnmath16 View Post
    How do you solve these corresponding equations (will use the values of y and x to graph)

    3x-y-=5 and x+3y=6

    I've figured out how to solve 3x-y=5 by doing this:
    3x-y=5
    y=3x-5

    But what about the other one? (x+3y=6)
    this here is a common linear system.
    there are three ways to solve, elimination, substitution, and by graphing

    I will use substitution since it is easiest for this linear system

    y=3x-5
    x+3y=6
    plug the value of y into the second equation

    x+3(3x-5)=6
    x+9x-15=6
    10x=6+15
    x=21/10
    x=2.1

    take that value and plug it into the other equation

    y=3(2.1)-5
    y=6.3-5
    y=1.3

    Thefore, the answer is (2.1,1.3)
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