document.write( "Question 62919: find k so the system is inconsistent:
\n" ); document.write( "x-6ky=5k
\n" ); document.write( "(k+10)y=(k-1)x-(k+8)
\n" ); document.write( "thanks so much for your help! \n" ); document.write( "
Algebra.Com's Answer #43771 by venugopalramana(3286)\"\" \"About 
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find k so the system is inconsistent:
\n" ); document.write( " x-6ky=5k..........................1
\n" ); document.write( " (k+10)y=(k-1)x-(k+8)...OR\r
\n" ); document.write( "\n" ); document.write( "X(K-1)-Y(K+10)=K+8................2
\n" ); document.write( "FOR THE EQNS. TO BE INCONSISTENT, RATIO OF COEFFICIENTS OF UNKNOWNS(RU SAY) SHOULD
\n" ); document.write( "BE EQUAL WHILE RATIO OF CONSTANTS (RC SAY) SHOULD BE DIFFERENT.
\n" ); document.write( " RU = (K-1)/1 =(K+10)/6K
\n" ); document.write( "6K^2-6K = K+10
\n" ); document.write( "6K^2-7K-10=0
\n" ); document.write( "6K^2-12K+5K-10=0
\n" ); document.write( "6K(K-2)+5(K-2)=0
\n" ); document.write( "(K-2)(6K+5)=0
\n" ); document.write( "K=2....OR.....K= -5/6
\n" ); document.write( "HENCE ...
\n" ); document.write( "AT K=2.....
\n" ); document.write( "RU = (2-1)/1=1
\n" ); document.write( "AND
\n" ); document.write( "RC = (K+8)/5K = (2+8)/5*2=1....
\n" ); document.write( "RU = RC= 1
\n" ); document.write( "HENCE NOT SUITABLE \r
\n" ); document.write( "\n" ); document.write( "AT K=-5/6
\n" ); document.write( "RU = (-5/6 -1)/1 = -11/6
\n" ); document.write( "RC = (-5/6 +8)/(5*-5/6)=(43/6)/(-25/6)=-43/25
\n" ); document.write( "RU IS NOT EQUAL TO RC
\n" ); document.write( "HENCE THIS IS SUITABLE.
\n" ); document.write( "SO AT K = -5/6..........THE EQNS. ARE INCONSISTENT. \n" ); document.write( "
\n" );