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