Posted by **True** on Sunday, July 22, 2012 at 6:09pm.

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 -
**MathMate**, Sunday, July 22, 2012 at 6:33pm
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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