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29 July, 13:26

Which values for A and B will create infinitely many solutions for this system of equations?

Ax-y=8

2x+y=B

A = 2. B - 8

A=-2. B=8

A = 2. B=-8

A--2.8--8

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Answers (1)
  1. 29 July, 13:30
    0
    see explanation below

    Step-by-step explanation:

    Let's write again the system:

    Ax - y = 8

    2x + y = B

    Now we want to know which values for A and B will turn the system with infinite solutions. To know this, we need to apply the following. A system of equation has the following general expression:

    ax + by = e

    cx + dy = f

    To know if a system has infinite solutions, we have to acomplish the following:

    a * d = b * c and b * f = d * e

    so, let's replace the options into these expression, and the ones who match this, would be the values of A and B:

    1. A = 2 and B = - 8

    2x - y = 8

    2x + y = - 8

    a * d = b * c

    a * d = 2 * 1 = 2

    b * c = - 1 * 2 = - 2

    These are not the same, so we can discart this option.

    2. A = - 2 B = 8

    -2x - y = 8

    2x + y = 8

    a * d = b * c

    a * d = - 2 * 1 = - 2

    b * c = - 1 * 2 = - 2

    This match, let's see the other

    b * f = d * e

    b * f = (-1) * (-8) = 8

    d * e = 1 * 8 = 8

    This option perfectly match, so this is the correct option. A = - 2 and B = 8
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