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Math Help - Linear systems?

  1. #1
    Junior Member
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    Linear systems?

    Show whether (0, 3) is the solution of the linear system below:
    2x+y=-3
    X+2y=8



    How would you do this?
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  2. #2
    Junior Member SirOJ's Avatar
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    (0,3) is the point so you want to see if this point is on the lines given. Here 0 is your x coordinate and 3 is your u coordinate
    You simply fill 0 and 3 wherever there is an x and y respectively in the line equations and if the line is = 0 then it is the linear solution
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  3. #3
    Super Member bigwave's Avatar
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    already answered
    Last edited by bigwave; December 14th 2009 at 02:21 PM. Reason: already answered
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  4. #4
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    Substitute x = 0 and y = 3 in the first equation.

    2x + y = -3

    2(0) + 3 = -3

    0 + 3 = -3

    3 = -3

    Because three does not equal the opposite of three, the equation 3 = -3 is false. Therefore, the point (0,3) is not a solution to the system of linear equations.

    If the equation were true, then substitute x = 0 and y = 3 in the second equation. If that equation were true, then the point (0,3) would be a solution of the system of linear equations.

    In general, substitute (x,y) in each equation of the system. If the substitution produces an invalid equation, then the point (x,y) is not a solution to the system of equations. If the substitution produces a valid equation, then the point (x,y) is a solution to the system of equations.
    Last edited by NOX Andrew; December 14th 2009 at 06:43 PM.
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