SOLUTION: find k so the system is inconsistent: x-6ky=5k (k+10)y=(k-1)x-(k+8) thanks so much for your help!

Question 62919: find k so the system is inconsistent:
x-6ky=5k
(k+10)y=(k-1)x-(k+8)
thanks so much for your help!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
find k so the system is inconsistent:
x-6ky=5k..........................1
(k+10)y=(k-1)x-(k+8)...OR
X(K-1)-Y(K+10)=K+8................2
FOR THE EQNS. TO BE INCONSISTENT, RATIO OF COEFFICIENTS OF UNKNOWNS(RU SAY) SHOULD
BE EQUAL WHILE RATIO OF CONSTANTS (RC SAY) SHOULD BE DIFFERENT.
RU = (K-1)/1 =(K+10)/6K
6K^2-6K = K+10
6K^2-7K-10=0
6K^2-12K+5K-10=0
6K(K-2)+5(K-2)=0
(K-2)(6K+5)=0
K=2....OR.....K= -5/6
HENCE ...
AT K=2.....
RU = (2-1)/1=1
AND
RC = (K+8)/5K = (2+8)/5*2=1....
RU = RC= 1
HENCE NOT SUITABLE
AT K=-5/6
RU = (-5/6 -1)/1 = -11/6
RC = (-5/6 +8)/(5*-5/6)=(43/6)/(-25/6)=-43/25
RU IS NOT EQUAL TO RC
HENCE THIS IS SUITABLE.
SO AT K = -5/6..........THE EQNS. ARE INCONSISTENT.
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