ALGEBRA 2

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For what value of k does the system below not have a unique solution?
-1x + 7y + 2z = 6
2x + 1y + kz = -11
3x - 6y - 2z = -25

A.5
B.0
C.-2
D.-8

  • ALGEBRA 2 -

    A system of equations does not have a unique solution when the equations are not linearly independent. The equations are linearly independent if none of the left-hand side of the equations can be represented as a linear combination of the others.

    If we add equations (1) and (3)
    -1x + 7y + 2z = 6 ...(1)
    3x - 6y - 2z = -25 ...(3)

    we get
    2x +1y + 0z = -19 ...(2A)

    Examine the left-hand side of equation (2A) carefully.

    What value of k in equation (2) would make its left-hand side identical to a linear combination of (1) and (3), namely equation (2A)?

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