SOLUTION: When does the system {{{kx+3y=-6}}} {{{x+(k+2)y=2}}} have a unique solution? Thanks :)

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Question 444233: When does the system
kx%2B3y=-6
x%2B%28k%2B2%29y=2
have a unique solution?
Thanks :)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
When does the system
kx+3y=-6
x+(k+2)y=2
have a unique solution?
-----------------------------
The slopes must be different.
y = (-6-kx)/3
slope = -k/3
----------------------
y = (-x+2)/(k+2)
slope = -1/(k+2)
--------------------
Solve:
-k/3 = -1/(k+2)
Cross-multiply:
-k^2-2k = -3
k^2+2k-3 = 0
(k+3)(k-1) = 0
k = -3 or k = 1
-----------------------
The system has a unique solution as long as
k does not = -3 or 1.
===========================
Cheers,
Stan H.