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21 April, 20:18

Without graphing, is each system independent, dependent, or inconsistent? { - x-3y=0 x-y=4

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  1. 21 April, 20:36
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    Since we can find a solution for this system of equations we can affirm this is an independent system with solution equal to (x, y) = (3,-1)

    * If we graph a dependent system in the slope - intercept form, we can see that the graphs of each one are identical to each (beacuse we are representing the same line).

    *An inconsistent system occurs when the equations have the same slope, but different values of intersection with the Y axis.
  2. 21 April, 20:46
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    First, determine if there is a solution to the equation by finding their intersection. If we are to rewrite the system of linear equations,

    -x - 3y = 0

    x - y = 4

    The values of x and y from the equation are 3 and - 1. The slopes of the equations, m, are also not the same as shown below,

    m = - A/B

    where A and B are the numerical coefficients of x and y, respectively.

    m1 = - (-1/-3) = - 1/3

    m2 = - (1/-4) = 1/4

    Hence, the equations are independent.
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