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Math Help - Solve each of the following systems by addition

  1. #1
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    Solve each of the following systems by addition

    If a unique solution does not exist, state whether the system is inconsistent or dependent.


    1. 2x + 3y = 1
    5x + 3y = 16

    This is what I came up with, but I can not seem to make it work so I think the equation is inconsistent. Am I right or wrong? I didn't want to try question #2 because I am having a hard time with #1


    2x + 3y = 1
    -5x - 3y = -16
    -3x =-15
    x= 5





    2. x + 5y = 10
    -2x -10y = -20
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  2. #2
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    Quote Originally Posted by Patience View Post
    If a unique solution does not exist, state whether the system is inconsistent or dependent.


    1. 2x + 3y = 1
    5x + 3y = 16

    This is what I came up with, but I can not seem to make it work so I think the equation is inconsistent. Am I right or wrong? I didn't want to try question #2 because I am having a hard time with #1


    2x + 3y = 1
    -5x - 3y = -16
    -3x =-15
    x= 5





    2. x + 5y = 10
    -2x -10y = -20


    There is nothing wrong with your analysis of #1. After adding, you (correctly) got x=5. All that's left to do is substitute 5 back into either of the original equations to find the y value of the point.

    As for the second, you should notice that the second equation is simply the first with eqch term multiplied by -2. Divide both sides by -2 and you will have two of the same equation. Since they are the same line, any point on that line satisfies both and the system is therefore depenent.

    -Pulsar
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