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Geometric representations of simultaneous equations watch

    • Thread Starter

    I've found myself with the simultaneous equations

    3x + 2y - z = 10
    5x - y - 4z = 17
    x + 5y + 2z = b

    I think the equations are inconsistent unless b = 3.

    Given that the equations represent three planes having a common line of intersection, find the line in the (x - p)/l = (y - q)/m = (z - r)/n form.

    I think they're referring to the case b = 3 here, since any other case the equations have no solutions and the planes don't intersect. I'm stuck on how to find the line of the solutions in the case where b = 3, I've never been taught this. (Or roots of unity for that matter. Neglegant teacher?)

    well, stick b=3 in. then try and solve the equations normally, but you will be left with a relation between x,y, and z, which will be the equation of the line that they are asking you to look for.

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