document.write( "Question 1206698: Find all values of k for which the given the augmented matrix corresponds to a consistent linear system
\n" ); document.write( " K 1 -2
\n" ); document.write( " 4 -1 2 \n" ); document.write( "

Algebra.Com's Answer #844290 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"matrix%282%2C3%2Ck%2C+1%2C+-2%2C%0D%0A4%2C+-1%2C+2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "system is:\r
\n" ); document.write( "\n" ); document.write( " $\"kx%2By=-2\"$ ....eq.1
\n" ); document.write( " $\"4x-y=2\"$ .....eq.2
\n" ); document.write( "----------\r
\n" ); document.write( "\n" ); document.write( " $\"kx%2By=-2\"$ ...eq.1, solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=%28-2-y%29%2Fk\"$ ....eq.1a\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4x-y=2\"$ .....eq.2, solve for $\"x\"$
\n" ); document.write( " $\"x=%282%2By%29%2F4\"$ .....eq.2a\r
\n" ); document.write( "\n" ); document.write( "from eq.1a and eq.2a we have\r
\n" ); document.write( "\n" ); document.write( " $\"%28-2-y%29%2Fk=%282%2By%29%2F4\"$ ....., solve for $\"k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4%28-2-y%29=k%282%2By%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-4%282%2By%29=k%282%2By%29\"$ ....both sides divide by $\"2%2By\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-4=k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=-4\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );